115 (number)

← 114 115 116 →
Cardinal one hundred fifteen
Ordinal 115th
(one hundred and fifteenth)
Factorization 5 × 23
Divisors 1, 5, 23, 115
Roman numeral CXV
Binary 11100112
Ternary 110213
Quaternary 13034
Quinary 4305
Senary 3116
Octal 1638
Duodecimal 9712
Hexadecimal 7316
Vigesimal 5F20
Base 36 3736

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

In mathematics

115 has a square sum of divisors:

\sigma(115)=1+5+23+115=144=12^2.

It is unknown whether the set of numbers with this property is infinite, but this would follow from the truth of the Bunyakovsky conjecture on polynomials with infinitely many prime values.[1]

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

is a prime number.[6]

In other fields

115 is also the fire service emergency number in Mauritius[7] and Italy,[8] and the ambulance emergency number in Vietnam.[9]

See also

References

  1. ↑ "Sloane's A006532 : Numbers n such that sum of divisors of n is a square", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ↑ "Sloane's 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's 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's A002369 : Number of ways of folding a strip of n rectangular stamps", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ↑ "Sloane's 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's A002234 : Numbers n such that the Woodall number n*2^n - 1 is prime", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. ↑ Cheong-Lum, Roseline Ng (2009), CultureShock! Mauritius: A Survival Guide to Customs and Etiquette, Marshall Cavendish International Asia Pte Ltd, p. 287, ISBN 9789814435604.
  8. ↑ DK Eyewitness Travel Guide: Italy, Penguin, 2013, p. 619, ISBN 9781465414946.
  9. ↑ The Rough Guide to Southeast Asia On A Budget, Penguin, 2014, p. 1286, ISBN 9780241012727.
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