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# 115 (number)

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### 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
Vigesimal 5F20
Base 36 3736

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

## Contents

• In mathematics 1
• In other fields 2
• References 4

## 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]

## 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, .
8. ^ DK Eyewitness Travel Guide: Italy, Penguin, 2013, p. 619, .
9. ^ The Rough Guide to Southeast Asia On A Budget, Penguin, 2014, p. 1286, .
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