115 (number)

← 114 115 116 →
← 110 111 112 113 114 115 116 117 118 119 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred fifteen
Ordinal	115th (one hundred fifteenth)
Factorization	5 × 23
Divisors	1, 5, 23, 115
Greek numeral	ΡΙΕ´
Roman numeral	CXV, cxv
Binary	11100112
Ternary	110213
Senary	3116
Octal	1638
Duodecimal	9712
Hexadecimal	7316

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

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.

See also

• 115 (disambiguation)

References

1. Sloane, N. J. A. (ed.). "SequenceA006532(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.). "SequenceA000081(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.). "SequenceA000903(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.). "SequenceA002369(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.). "SequenceA002413(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.). "SequenceA002234(Numbers n such that the Woodall number n*2^n - 1 is prime)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.