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Natural number

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

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]

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