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115 (number) - Wikipedia

From Wikipedia, the free encyclopedia

Natural number

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

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

σ ( 115 ) = 1 + 5 + 23 + 115 = 144 = 12 2 . {\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,

115 ⋅ 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)

Integers −1 0s

1000
- 1001
- 1023
- 1024
- 1089
- 1093
- 1105
- 1234
- 1289
- 1458
- 1510
- 1728
- 1729
- 1980
- 1987
2000
- 2016
- 2520
3000
- 3511
4000
- 4104
5000
- 5040
6000
- 6174
7000
- 7744
- 7825
8000
- 8128
- 8192
9000
- 9855
- 9999

10,000
- 16,807
20,000
30,000
40,000
50,000
60,000
- 64,079
- 65,535
- 65,536
- 65,537
70,000
80,000
90,000

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