# 115 (number)

From HandWiki

__: Natural number__

**Short description**
| ||||
---|---|---|---|---|

Cardinal | one hundred fifteen | |||

Ordinal | 115th (one hundred fifteenth) | |||

Factorization | 5 × 23 | |||

Divisors | 1, 5, 23, 115 | |||

Greek numeral | ΡΙΕ´ | |||

Roman numeral | CXV | |||

Binary | 1110011_{2} | |||

Ternary | 11021_{3} | |||

Quaternary | 1303_{4} | |||

Quinary | 430_{5} | |||

Senary | 311_{6} | |||

Octal | 163_{8} | |||

Duodecimal | 97_{12} | |||

Hexadecimal | 73_{16} | |||

Vigesimal | 5F_{20} | |||

Base 36 | 37_{36} |

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

## In mathematics

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

- [math]\displaystyle{ \sigma(115)=1+5+23+115=144=12^2. }[/math]

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,

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

is a prime number.^{[6]}
115 is the sum of the first five heptagonal numbers.

## See also

- 115 (disambiguation)

## References

- ↑ Sloane, N. J. A., ed. "Sequence A006532 (Numbers n such that sum of divisors of n is a square)". OEIS Foundation. https://oeis.org/A006532.
- ↑ Sloane, N. J. A., ed. "Sequence A000081 (Number of rooted trees with n nodes (or connected functions with a fixed point))". OEIS Foundation. https://oeis.org/A000081.
- ↑ Sloane, N. J. A., ed. "Sequence A000903 (Number of inequivalent ways of placing n nonattacking rooks on n X n board)". OEIS Foundation. https://oeis.org/A000903.
- ↑ Sloane, N. J. A., ed. "Sequence A002369 (Number of ways of folding a strip of n rectangular stamps)". OEIS Foundation. https://oeis.org/A002369.
- ↑ Sloane, N. J. A., ed. "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers: n*(n+1)*(5*n-2)/6)". OEIS Foundation. https://oeis.org/A002413.
- ↑ Sloane, N. J. A., ed. "Sequence A002234 (Numbers n such that the Woodall number n*2^n - 1 is prime)". OEIS Foundation. https://oeis.org/A002234.

Original source: https://en.wikipedia.org/wiki/115 (number).
Read more |