114 (number)
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From Wikipedia, the free encyclopedia
Natural number
| Cardinal | one hundred fourteen |
|---|---|
| Ordinal | 114th (one hundred fourteenth) |
| Factorization | 2 ×ばつ 3 ×ばつ 19 |
| Divisors | 1, 2, 3, 6, 19, 38, 57, 114 |
| Greek numeral | ΡΙΔ ́ |
| Roman numeral | CXIV, cxiv |
| Binary | 11100102 |
| Ternary | 110203 |
| Senary | 3106 |
| Octal | 1628 |
| Duodecimal | 9612 |
| Hexadecimal | 7216 |
114 (one hundred [and] fourteen) is the natural number following 113 and preceding 115.
In mathematics
[edit ]- 114 is an abundant number, a sphenic number [1] and a Harshad number.[2] It is the sum of the first four hyperfactorials, including H(0). At 114, the Mertens function sets a new low of -6, a record that stands until 197.
- 114 is the smallest positive integer* which has yet to be represented as a3 + b3 + c3, where a, b, and c are integers. It is conjectured that 114 can be represented this way. (*Excluding integers of the form 9k ± 4, for which solutions are known not to exist.)[3]
- There is no answer to the equation φ(x) = 114, making 114 a nontotient.[4]
- 114 appears in the Padovan sequence,[5] preceded by the terms 49, 65, 86 (it is the sum of the first two of these).
- 114 is a repdigit in base 7 (222).
See also
[edit ]References
[edit ]- ^ Sloane, N. J. A. (ed.). "Sequence A007304 (Sphenic numbers: products of 3 distinct primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005349 (Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
- ^ Houston, Robin (2019年09月06日). "42 is the answer to the question "what is (-80538738812075974)3 + 804357581458175153 + 126021232973356313?"". The Aperiodical. Retrieved 2019年12月28日.
- ^ Sloane, N. J. A. (ed.). "Sequence A005277 (Nontotients: even numbers k such that phi(m) = k has no solution)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000931 (Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
