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35 (number)

From Wikipedia, the free encyclopedia
Natural number
← 3435 36 →
Cardinalthirty-five
Ordinal35th
(thirty-fifth)
Factorization5 × 7
Divisors1, 5, 7, 35
Greek numeralΛΕ´
Roman numeralXXXV,xxxv
Binary1000112
Ternary10223
Senary556
Octal438
Duodecimal2B12
Hexadecimal2316

35 (thirty-five) is thenatural number following34 and preceding36.

In mathematics

[edit]
35 is a tetrahedral number.
The 35 free hexominoes

35 is the sum of the first fivetriangular numbers, making it atetrahedral number.[1]

35 is the 10th discretesemiprime (5×7{\displaystyle 5\times 7})[2] and the first with5 as the lowest non-unitary factor, thus being the first of the form (5.q) where q is a higher prime.

35 has twoprime factors, (5 and7) which also form its main factor pair (5 x 7) and comprise the secondtwin-prime distinctsemiprime pair.

The aliquot sum of 35 is13, within analiquot sequence of only one composite number (35,13,1,0) to the Prime in the13-aliquot tree. 35 is the secondcomposite number with the aliquot sum13; the first being the cube27.

35 is the last member of the first triple cluster of semiprimes33,34, 35. The second such triple distinct semiprime cluster is85,86, and87.[3]

35 is the number of ways that three things can be selected from a set of seven unique things, also known as the "combination of seven things taken three at a time".

The sentence "This sentence is thirty-five letters long" is 35 letters long (excluding spaces and hyphen), otherwise known as anautogram.

35 is acentered cube number,[4] acentered tetrahedral number, apentagonal number,[5] and apentatope number.[6]

35 is ahighly cototient number, since there are more solutions to the equationxφ(x)=35{\displaystyle x-\varphi (x)=35} than there are for any other integers below it except 1.[7]

There are 35 freehexominoes, thepolyominoes made from six squares.

Since the greatest prime factor of352+1=1226{\displaystyle 35^{2}+1=1226} is 613, which is more than 35 twice, 35 is aStørmer number.[8]

35 is the highest number one can count to on one's fingers usingsenary.

35 is the number of quasigroups of order 4.

35 is the smallestcomposite number of the form6k+5{\displaystyle 6k+5}, wherek is a non-negative integer.

References

[edit]
  1. ^"Sloane's A000292 : Tetrahedral numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-31.
  2. ^Sloane, N. J. A. (ed.)."Sequence A001358".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A001748".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^"Sloane's A005898 : Centered cube numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-31.
  5. ^"Sloane's A000326 : Pentagonal numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-31.
  6. ^"Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-31.
  7. ^"Sloane's A100827 : Highly cototient numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-31.
  8. ^"Sloane's A005528 : Størmer numbers".The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-31.
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