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900 (number)

From Wikipedia, the free encyclopedia
(Redirected from969 (number))
For the year 900, see900 BC and900 AD.
"976 (number)" redirects here and is not to be confused with976 number.
Natural number
← 899900 901 →
Cardinalnine hundred
Ordinal900th
(nine hundredth)
Factorization22 × 32 × 52
Divisors1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
Greek numeralϠ´
Roman numeralCM,cm
Binary11100001002
Ternary10201003
Senary41006
Octal16048
Duodecimal63012
Hexadecimal38416
ArmenianՋ
Hebrewתת"ק / ץ
Babylonian cuneiform𒌋𒐙
Egyptian hieroglyph𓍪

900 (nine hundred) is thenatural number following899 and preceding901. It is thesquare of30 and the sum ofEuler's totient function for the first 54positive integers. In base 10, it is aHarshad number. It is also the first number to be the square of asphenic number.

In other fields

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900 is also:

Integers from 901 to 999

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900s

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910s

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  • 910 = 2 × 5 × 7 × 13, Mertens function(910) returns 0, Harshad number,happy number, balanced number,[9] number of polynomial symmetric functions of matrix of order 7 under separate row and column permutations[10]
  • 911 =Sophie Germain prime number, also theemergency telephone number in North America
  • 912 = 24 × 3 × 19, sum of four consecutive primes (223 + 227 + 229 + 233), sum of ten consecutive primes (71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109), Harshad number.
  • 913 = 11 × 83,Smith number,[11] Mertens function(913) returns 0.
  • 914 = 2 × 457, nontotient, number of compositions of 11 that are neither weakly increasing nor weakly decreasing[12]
  • 915 = 3 × 5 × 61, sphenic number, Smith number,[11] Mertens function(915) returns 0, Harshad number
  • 916 = 22 × 229, Mertens function(916) returns 0, nontotient,strobogrammatic, member of theMian–Chowla sequence[13]
  • 917 = 7 × 131, sum of five consecutive primes (173 + 179 + 181 + 191 + 193)
  • 918 = 2 × 33 × 17, Harshad number
  • 919 = prime number,cuban prime,[14]prime index prime,Chen prime,palindromic prime,centered hexagonal number,[15] Mertens function(919) returns 0

920s

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930s

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  • 930 = 2 × 3 × 5 × 31,pronic number[24]
  • 931 = 72 × 19; sum of three consecutive primes (307 + 311 + 313); doublerepdigit, 11130 and 77711; number of regular simple graphs spanning 7 vertices[25]
  • 932 = 22 × 233, number of regular simple graphs on 7 labeled nodes[26]
  • 933 = 3 × 311
  • 934 = 2 × 467, nontotient
  • 935 = 5 × 11 × 17, sphenic number,Lucas–Carmichael number,[27] Harshad number
  • 936 = 23 × 32 × 13,pentagonal pyramidal number,[28] Harshad number
  • 937 = prime number, Chen prime,star number,[29]happy number
  • 938 = 2 × 7 × 67, sphenic number, nontotient, number of lines through at least 2 points of an 8 × 8 grid of points[30]
  • 939 = 3 × 313, number of V-toothpicks after 31 rounds of the honeycomb sequence[31]

940s

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950s

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  • 950 = 2 × 52 × 19, nontotient,generalized pentagonal number[42]
  • 951 = 3 × 317,centered pentagonal number[43]
    • one of two ISBN Group Identifiers for books published in Finland
  • 952 = 23 × 7 × 17, number of reduced words of length 3 in the Weyl group D_17,[44] number of regions in regular tetradecagon with all diagonals drawn.[45]
    • 952 is also9-5-2, acard game similar tobridge.
    • one of two ISBN Group Identifiers for books published in Finland
  • 953 = prime number, Sophie Germain prime,[46] Chen prime, Eisenstein prime with no imaginary part,centered heptagonal number[47]
    • ISBN Group Identifier for books published inCroatia
  • 954 = 2 × 32 × 53, sum of ten consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), nontotient, Harshad number, sixth derivative of x^(x^x) at x=1.[48]
  • 955 = 5 × 191, number of transitive rooted trees with 17 nodes
    • ISBN Group Identifier for books published in Sri Lanka
  • 956 = 22 × 239, number of compositions of 13 into powers of 2.[49]
    • ISBN Group Identifier for books published in Chile
  • 957 = 3 × 11 × 29, sphenic number, antisigma(45)[50]
    • one of two ISBN Group Identifiers for books published in Taiwan and China
  • 958 = 2 × 479, nontotient,Smith number[11]
  • 959 = 7 × 137, composite de Polignac number[51]
    • ISBN Group Identifier for books published in Cuba

960s

[edit]
  • 960 = 26 × 3 × 5, sum of six consecutive primes (149 + 151 + 157 + 163 + 167 + 173), Harshad number
    • country calling code for Maldives, ISBN Group Identifier for books published in Greece
    • The number of possible starting positions for the chess variantChess960
  • 961 = 312, the largest 3-digit perfect square, sum of three consecutive primes (313 + 317 + 331), sum of five consecutive primes (181 + 191 + 193 + 197 + 199),centered octagonal number[52]
    • country calling code for Lebanon, ISBN Group Identifier for books published inSlovenia
  • 962 = 2 × 13 × 37, sphenic number, nontotient
    • country calling code for Jordan, one of two ISBN Group Identifiers for books published in Hong Kong
  • 963 = 32 × 107, sum of the first twenty-four primes
    • country calling code for Syria, ISBN Group Identifier for books published in Hungary
  • 964 = 22 × 241, sum of four consecutive primes (233 + 239 + 241 + 251), nontotient, totient sum for first 56 integers
    • country calling code for Iraq, ISBN Group Identifier for books published in Iran,happy number
  • 965 = 5 × 193
    • country calling code for Kuwait, ISBN Group Identifier for books published in Israel
  • 966 = 2 × 3 × 7 × 23 ={83}{\displaystyle \left\{{8 \atop 3}\right\}}, sum of eight consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137 + 139), Harshad number
    • country calling code for Saudi Arabia, one of two ISBN Group Identifiers for books published in Ukraine
  • 967 = prime number,prime index prime
    • country calling code for Yemen, one of two ISBN Group Identifiers for books published in Malaysia
  • 968 = 23 × 112, nontotient,Achilles number, area of a square with diagonal 44[53]
    • country calling code for Oman, one of two ISBN Group Identifiers for books published in Mexico
  • 969 = 3 × 17 × 19, sphenic number,nonagonal number,[54]tetrahedral number[55]

970s

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  • 970 = 2 × 5 × 97, sphenic number,heptagonal number
    • country calling code for Palestinian territories, one of two ISBN Group Identifiers for books published in Mexico
  • 971 = prime number, Chen prime, Eisenstein prime with no imaginary part
    • country calling code for United Arab Emirates, ISBN Group Identifier for books published in the Philippines
  • 972 = 22 × 35, Harshad number,Achilles number
    • country calling code for Israel, one of two ISBN Group Identifiers for books published in Portugal
      • The Sum of Anti-Factors of 972 = number * (n/2) where n is an Odd number. So, it is a Hemi-Anti-Perfect Number. Other such Numbers include 2692, etc.

972 has Anti-Factors = 5, 8, 24, 29, 67, 72, 216, 389, 648

Sum of Anti-Factors = 5 + 8 + 24 + 29 + 67 + 72 + 216 + 389 + 648 = 1458 = 972 * 3/2

980s

[edit]

990s

[edit]
  • 990 = 2 × 32 × 5 × 11, sum of six consecutive primes (151 + 157 + 163 + 167 + 173 + 179), 44thtriangular number,[4] Harshad number
  • 991 = prime number, sum of five consecutive primes (191 + 193 + 197 + 199 + 211), sum of seven consecutive primes (127 + 131 + 137 + 139 + 149 + 151 + 157), Chen prime, lucky prime,prime index prime
  • 992 = 25 × 31,pronic number,[24] nontotient; number of eleven-dimensionalexotic spheres.[69]
    • country calling code for Tajikistan
  • 993 = 3 × 331
    • country calling code for Turkmenistan
  • 994 = 2 × 7 × 71, sphenic number, nontotient, number of binary words of length 13 with all distinct runs.[70]
    • country calling code for Azerbaijan
  • 995 = 5 × 199
    • country calling code for Georgia
    • Singapore fire brigade and emergency ambulance services hotline,Brunei Darussalam fire service emergency number
  • 996 = 22 × 3 × 83
    • country calling code for Kyrgyzstan
  • 997 = largest three-digit prime number, strictly non-palindromic number.[59] It is also alucky prime.
  • 998 = 2 × 499, nontotient, number of 7-node graphs with two connected components.[71]
    • country calling code for Uzbekistan
Main article:999 (number)

References

[edit]
Wikimedia Commons has media related to900 (number).
  1. ^"Pay-Per-Call Information Services".Federal Communications Commission. 2011-02-11. Retrieved2021-03-31.
  2. ^"Bowler throws 36 consecutive strikes for incredible 900 series".For The Win. 2016-01-13. Retrieved2021-03-31.
  3. ^Sawan, Amer (2024-06-14)."How Old is Yoda in The Phantom Menace?".CBR. Retrieved2025-04-19.
  4. ^abc"Sloane's A000217: Triangular numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  5. ^Sloane, N. J. A. (ed.)."Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. ^"Sloane's A098237: Composite de Polignac numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-10.
  7. ^abSloane, N. J. A. (ed.)."Sequence A006245 (Number of primitive sorting networks on n elements; also number of rhombic tilings of a 2n-gon)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-24.
  8. ^Sloane, N. J. A. (ed.)."Sequence A303546 (Number of non-isomorphic aperiodic multiset partitions of weight n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-24.
  9. ^Sloane, N. J. A. (ed.)."Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^Sloane, N. J. A. (ed.)."Sequence A007716 (Number of polynomial symmetric functions of matrix of order n under separate row and column permutations)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  11. ^abcde"Sloane's A006753 : Smith numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  12. ^Sloane, N. J. A. (ed.)."Sequence A332834 (Number of compositions of n that are neither weakly increasing nor weakly decreasing)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-23.
  13. ^"Sloane's A005282 : Mian-Chowla sequence".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  14. ^"Sloane's A002407 : Cuban primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  15. ^"Sloane's A003215 : Hex (or centered hexagonal) numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  16. ^Sloane, N. J. A. (ed.)."Sequence A055544 (Total number of nodes in all rooted trees with n nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-23.
  17. ^Sloane, N. J. A. (ed.)."Sequence A301462 (Number of enriched r-trees of size n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-23.
  18. ^Sloane, N. J. A. (ed.)."Sequence A030662 (Number of combinations of n things from 1 to n at a time, with repeats allowed)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-23.
  19. ^"Sloane's A000984 : Central binomial coefficients".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  20. ^"Sloane's A000326 : Pentagonal numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  21. ^"Sloane's A001844 : Centered square numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  22. ^"Sloane's A000073 : Tribonacci numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  23. ^"Sloane's A080076 : Proth primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  24. ^ab"Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  25. ^Sloane, N. J. A. (ed.)."Sequence A319612 (Number of regular simple graphs spanning n vertices)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-23.
  26. ^Sloane, N. J. A. (ed.)."Sequence A295193 (Number of regular simple graphs on n labeled nodes)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-22.
  27. ^"Sloane's A006972 : Lucas-Carmichael numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  28. ^"Sloane's A002411 : Pentagonal pyramidal numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  29. ^"Sloane's A003154 : Centered 12-gonal numbers. Also star numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  30. ^Sloane, N. J. A. (ed.)."Sequence A018808 (Number of lines through at least 2 points of an n X n grid of points)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-22.
  31. ^Sloane, N. J. A. (ed.)."Sequence A161206 (V-toothpick (or honeycomb) sequence)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^Sloane, N. J. A. (ed.)."Sequence A001628 (Convolved Fibonacci numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ^Sloane, N. J. A. (ed.)."Sequence A005727".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  34. ^"Sloane's A006882 : Double factorials".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  35. ^Higgins, Peter (2008).Number Story: From Counting to Cryptography. New York: Copernicus. p. 13.ISBN 978-1-84800-000-1.
  36. ^"Sloane's A006038 : Odd primitive abundant numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  37. ^"Sloane's A006036 : Primitive pseudoperfect numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  38. ^"Sloane's A076980 : Leyland numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  39. ^"Sloane's A000384 : Hexagonal numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  40. ^ab"Sloane's A006562 : Balanced primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  41. ^Sloane, N. J. A. (ed.)."Sequence A269134 (Number of combinatory separations of normal multisets of weight n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-13.
  42. ^Sloane, N. J. A. (ed.)."Sequence A001318 (Generalized pentagonal numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  43. ^"Sloane's A005891 : Centered pentagonal numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  44. ^Sloane, N. J. A. (ed.)."Sequence A162328 (Number of reduced words of length n in the Weyl group D_17)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-12.
  45. ^Sloane, N. J. A. (ed.)."Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-13.
  46. ^"Sloane's A005384 : Sophie Germain primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  47. ^"Sloane's A069099 : Centered heptagonal numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  48. ^Sloane, N. J. A. (ed.)."Sequence A179230".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-12.
  49. ^(sequenceA023359 in theOEIS)
  50. ^Sloane, N. J. A. (ed.)."Sequence A024816 (Antisigma(n): Sum of the numbers less than n that do not divide n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-11.
  51. ^"Sloane's A098237: Composite de Polignac numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-10.
  52. ^"Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  53. ^Sloane, N. J. A. (ed.)."Sequence A001105".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  54. ^"Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  55. ^"Sloane's A000292 : Tetrahedral numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  56. ^"A002982: Numbers n such that n! - 1 is prime".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-10.
  57. ^"Sloane's A001107 : 10-gonal (or decagonal) numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  58. ^"Sloane's A042978 : Stern primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  59. ^abc"Sloane's A016038 : Strictly non-palindromic numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  60. ^Sloane, N. J. A. (ed.)."Sequence A004148 (Generalized Catalan numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  61. ^"A008793".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-10.
  62. ^"Sloane's A005385 : Safe primes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  63. ^"Sloane's A001190 : Wedderburn-Etherington numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  64. ^"Sloane's A002559 : Markoff (or Markov) numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  65. ^"Sloane's A000129 : Pell numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  66. ^Sloane, N. J. A. (ed.)."Sequence A006330 (Number of corners, or planar partitions of n with only one row and one column)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  67. ^"Sloane's A000045 : Fibonacci numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  68. ^"Sloane's A0217719 : Extra strong Lucas pseudoprimes".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-11.
  69. ^"week164". Math.ucr.edu. 2001-01-13. Retrieved2014-05-12.
  70. ^"A351016".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-10.
  71. ^"A275165".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-10.
  72. ^"Sloane's A006886 : Kaprekar numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-06-02.
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