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# 115 (number)

 ← 114 115 116 →
Cardinalone hundred fifteen
Ordinal115th
(one hundred fifteenth)
Factorization5 × 23
Divisors1, 5, 23, 115
Greek numeralΡΙΕ´
Roman numeralCXV
Binary11100112
Ternary110213
Quaternary13034
Quinary4305
Senary3116
Octal1638
Duodecimal9712
Vigesimal5F20
Base 363736

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

## In mathematics

115 has a square sum of divisors:[1]

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

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,

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

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, N. J. A. (ed.). "Sequence A006532 (Numbers n such that sum of divisors of n is a square)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^
3. ^
4. ^
5. ^
6. ^
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.

This page was last edited on 21 March 2019, at 22:03
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