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
Binary	11100102
Ternary	110203
Senary	3106
Octal	1628
Duodecimal	9612
Hexadecimal	7216

Last updated November 26, 2024

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).

In religion

There are 114 chapters, or surahs, in the Quran.

There are 114 sayings in The Gospel of Thomas.

In science

114 is the atomic number of flerovium.

Related Research Articles

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200 is the natural number following 199 and preceding 201.

300 is the natural number following 299 and preceding 301.

360 is the natural number following 359 and preceding 361.

400 is the natural number following 399 and preceding 401.

500 is the natural number following 499 and preceding 501.

700 is the natural number following 699 and preceding 701.

600 is the natural number following 599 and preceding 601.

800 is the natural number following 799 and preceding 801.

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References

↑ Sloane, N. J. A. (ed.). "SequenceA007304(Sphenic numbers: products of 3 distinct primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
↑ 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.
↑ Houston, Robin (2019-09-06). "42 is the answer to the question "what is (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³?"". The Aperiodical. Retrieved 2019-12-28.
↑ 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.
↑ 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.

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[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.

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