115 (number)

From HandWiki
Short description: Natural number
← 114 115 116 →
Cardinalone hundred fifteen
Ordinal115th
(one hundred fifteenth)
Factorization5 × 23
Divisors1, 5, 23, 115
Greek numeralΡΙΕ´
Roman numeralCXV
Binary11100112
Ternary110213
Quaternary13034
Quinary4305
Senary3116
Octal1638
Duodecimal9712
Hexadecimal7316
Vigesimal5F20
Base 363736

115 (one hundred [and] fifteen) is the natural number following 114 and preceding 116.

In mathematics

115 has a square sum of divisors:[1]

σ(115)=1+5+23+115=144=122.

There are 115 different rooted trees with exactly eight nodes,[2] 115 inequivalent ways of placing six rooks on a 6 × 6 chess board in such a way that no two of the rooks attack each other,[3] and 115 solutions to the stamp folding problem for a strip of seven stamps.[4]

115 is also a heptagonal pyramidal number.[5] The 115th Woodall number,

115⋅2115−1=4776913109852041418248056622882488319,

is a prime number.[6] 115 is the sum of the first five heptagonal numbers.

See also

  • 115 (disambiguation)

References

  1. ↑ Sloane, N. J. A., ed. "Sequence A006532 (Numbers n such that sum of divisors of n is a square)". OEIS Foundation. https://oeis.org/A006532. 
  2. ↑ Sloane, N. J. A., ed. "Sequence A000081 (Number of rooted trees with n nodes (or connected functions with a fixed point))". OEIS Foundation. https://oeis.org/A000081. 
  3. ↑ Sloane, N. J. A., ed. "Sequence A000903 (Number of inequivalent ways of placing n nonattacking rooks on n X n board)". OEIS Foundation. https://oeis.org/A000903. 
  4. ↑ Sloane, N. J. A., ed. "Sequence A002369 (Number of ways of folding a strip of n rectangular stamps)". OEIS Foundation. https://oeis.org/A002369. 
  5. ↑ Sloane, N. J. A., ed. "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers: n*(n+1)*(5*n-2)/6)". OEIS Foundation. https://oeis.org/A002413. 
  6. ↑ Sloane, N. J. A., ed. "Sequence A002234 (Numbers n such that the Woodall number n*2^n - 1 is prime)". OEIS Foundation. https://oeis.org/A002234. 



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