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115 (number)

From Wikipedia, the free encyclopedia

Natural number
← 114115 116 →
Cardinalone hundred fifteen
Ordinal115th
(one hundred fifteenth)
Factorization5 × 23
Divisors1, 5, 23, 115
Greek numeralΡΙΕ´
Roman numeralCXV,cxv
Binary11100112
Ternary110213
Senary3116
Octal1638
Duodecimal9712
Hexadecimal7316

115 (one hundred [and] fifteen) is thenatural number following114 and preceding116.

In mathematics

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115 has asquare sum of divisors:[1]

σ(115)=1+5+23+115=144=122.{\displaystyle \sigma (115)=1+5+23+115=144=12^{2}.}

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

115 is also aheptagonal pyramidal number.[5] The 115thWoodall number,

115⋅2115−1=4776913109852041418248056622882488319,{\displaystyle 115\cdot 2^{115}-1=4\;776\;913\;109\;852\;041\;418\;248\;056\;622\;882\;488\;319,}

is aprime number.[6]115 is the sum of the first fiveheptagonal numbers.

See also

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References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A006532 (Numbers n such that sum of divisors of n is a square)".TheOn-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))".TheOn-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)".TheOn-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)".TheOn-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)".TheOn-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)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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