118_(number)

118 (number)

118 (number)

Natural number

118 (one hundred [and] eighteen) is the natural number following 117 and preceding 119.

Quick Facts ← 117 118 119 →, Cardinal ...

In mathematics

There is no answer to the equation φ(x) = 118, making 118 a nontotient.[1]

Four expressions for 118 as the sum of three positive integers have the same product:

14 + 50 + 54 = 15 + 40 + 63 = 18 + 30 + 70 = 21 + 25 + 72 = 118 and
14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800.

118 is the smallest number that can be expressed as four sums with the same product in this way.[2]

Because of its expression as 118 = 35 − 53, it is a Leyland number of the second kind.[3]

118!! - 1 is a prime number, where !! denotes the double factorial (the product of even integers up to 118).[4]

In other fields

See also

References

Wikimedia Commons has media related to 118 (number).
  1. [1]
    Sloane, N. J. A. (ed.). "Sequence A005277 (Nontotients)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. [2]
    Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134 - 135
  3. [3]
    Sloane, N. J. A. (ed.). "Sequence A045575 (Nonnegative numbers of the form x^y - y^x, for x,y > 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. [4]
    Sloane, N. J. A. (ed.). "Sequence A007749 (Numbers k such that k!! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
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