115 (number)
From HandWiki
Short description: Natural number
| ||||
|---|---|---|---|---|
| Cardinal | one hundred fifteen | |||
| Ordinal | 115th (one hundred fifteenth) | |||
| Factorization | 5 × 23 | |||
| Divisors | 1, 5, 23, 115 | |||
| Greek numeral | ΡΙΕ´ | |||
| 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:[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.
 |  |
