114 (number) explained

Number:	114
Divisor:	1, 2, 3, 6, 19, 38, 57, 114

114 (one hundred [and] fourteen) is the natural number following 113 and preceding 115.

In mathematics

• 114 is an abundant number, a sphenic number and a Harshad number. 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.)^[1]
• There is no answer to the equation φ(x) = 114, making 114 a nontotient.^[2]
• 114 appears in the Padovan sequence,^[3] 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.

See also

• 114 (disambiguation)

Notes and References

1. Web site: 42 is the answer to the question "what is (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³?". Houston. Robin. 2019-09-06. The Aperiodical. en. 2019-12-28.
2. Nontotients: even numbers k such that phi(m) = k has no solution.
3. Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0.