114 (number)

← 113 114 115 →
← 110 111 112 113 114 115 116 117 118 119 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred fourteen
Ordinal	114th (one hundred fourteenth)
Factorization	2 × 3 × 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

• 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

• 114 (disambiguation)

References

1. Sloane, N. J. A. (ed.). "SequenceA007304(Sphenic numbers: products of 3 distinct primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA005349(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.
3. Houston, Robin (2019-09-06). "42 is the answer to the question "what is (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³?"". The Aperiodical. Retrieved 2019-12-28.
4. Sloane, N. J. A. (ed.). "SequenceA005277(Nontotients: even numbers k such that phi(m) = k has no solution)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Sloane, N. J. A. (ed.). "SequenceA000931(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.