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115 (number)

Summary

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

 ← 114 115 116 →
Cardinalone hundred fifteen
Ordinal115th
(one hundred fifteenth)
Factorization5 × 23
Divisors1, 5, 23, 115
Greek numeralΡΙΕ´
Roman numeralCXV
Binary11100112
Ternary110213
Octal1638
Duodecimal9712
Hexadecimal7316

In mathematics

115 has a square sum of divisors:[1]

${\displaystyle \sigma (115)=1+5+23+115=144=12^{2}.}$

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,

${\displaystyle 115\cdot 2^{115}-1=4\;776\;913\;109\;852\;041\;418\;248\;056\;622\;882\;488\;319,}$

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

References

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