115 (number)

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

115 has a square sum of divisors:^[1]

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

There are 115 different rooted trees with exactly eight nodes,^[2] 115 inequivalent ways of placing six rooks on a 6 ×ばつ 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 rectangular stamps.^[4]

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

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

• 115 (disambiguation)