Natural number
Cardinal one hundred twenty-six Ordinal 126th Factorization 2 × 32 × 7 Divisors 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126 Greek numeral ΡΚϚ´ Roman numeral CXXVI ,cxxvi Binary 11111102 Ternary 112003 Senary 3306 Octal 1768 Duodecimal A612 Hexadecimal 7E16
126 (one hundred [and] twenty-six ) is thenatural number following125 and preceding127 .
As thebinomial coefficient ( 9 4 ) {\displaystyle {\tbinom {9}{4}}} central binomial coefficient , and inPascal's Triangle , it is apentatope number .[ 1] [ 2] sum of two cubes , and since 125 + 1 is σ3 (5), 126 is the fifth value of thesum of cubed divisors function .[ 3] [ 4]
126 is the fifthS {\displaystyle {\mathcal {S}}} Granville number , and the third such not to be a perfect number. Also, it is known to be the smallest Granville number with three distinct prime factors, and perhaps the only such Granville number.[ 5]
126 is apentagonal pyramidal number and adecagonal number .[ 6] [ 7] decagon into even polygons bydiagonals , and the number of crossing points among the diagonals of a regularnonagon .[ 8] [ 9]
There are exactly 126binary strings of length seven that are not repetitions of a shorter string, and 126 differentsemigroups on four elements (up toisomorphism and reversal).[ 10] [ 11]
There are exactly 126 positive integers that are not solutions of the equation
x = a b c + a b d + a c d + b c d , {\displaystyle x=abc+abd+acd+bcd,} wherea ,b ,c , andd must themselves all be positive integers.[ 12]
126 is the number ofroot vectors ofsimple Lie group E7
126 is the seventhmagic number innuclear physics . For each of these numbers, 2, 8, 20, 28, 50, 82, and 126, an atomic nucleus with this many protons is or is predicted to be more stable than for other numbers. Thus, although there has been no experimental discovery of element 126, tentatively calledunbihexium , it is predicted to belong to an island of stability that might allow it to exist with a long enoughhalf life that its existence could be detected.[ 13]
^ Sloane, N. J. A. (ed.)."Sequence A001405 (Central binomial coefficients)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.OEIS:A001700 for the odd central binomial coefficients.^ Deza, Elena ;Deza, M. (2012), "3.1 Pentatope numbers and their multidimensional analogues",Figurate Numbers , World Scientific, p. 162,ISBN 9789814355483 Sloane, N. J. A. (ed.)."Sequence A000332 (Binomial coefficients binomial(n,4))" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A003325 (Numbers that are the sum of 2 positive cubes)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A001158 (sigma_3(n): sum of cubes of divisors of n)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ de Koninck, Jean-Marie (2008).Those Fascinating Numbers American Mathematical Society . p. 40.ISBN 978-0-8218-4807-4 MR 2532459 .OCLC 317778112 .^ Deza & Deza (2012) , pp. 93, 211.Sloane, N. J. A. (ed.)."Sequence A002411 (Pentagonal pyramidal numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Deza & Deza (2012) , pp. 2–3 and 6;Sloane, N. J. A. (ed.)."Sequence A001107 (10-gonal (or decagonal) numbers)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A003168 (Number of blobs with 2n+1 edges)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A006561 (Number of intersections of diagonals in the interior of regular n-gon)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A027375 (Number of aperiodic binary strings of length n; also number of binary sequences with primitive period n)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A001423 (Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator))" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.^ Sloane, N. J. A. (ed.)."Sequence A027566 (Number of numbers not of form k_1 k_2 .. k_n (1/k_1 + .. + 1/k_n), k_i >= 1)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation.OEIS:A027563 for the list of these 126 numbers.^ Emsley, John (2011),Nature's Building Blocks: An A-Z Guide to the Elements ISBN 9780199605637
400 to 999
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100,000s to 10,000,000,000,000s
100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000
