118 (number)

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← 117 118 119 →
Cardinal one hundred eighteen
Ordinal 118th
(one hundred eighteenth)
Factorization 2 × 59
Divisors 1, 2, 59, 118
Greek numeral ΡΙΗ´
Roman numeral CXVIII, cxviii
Binary 11101102
Ternary 111013
Senary 3146
Octal 1668
Duodecimal 9A12
Hexadecimal 7616

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

Contents

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]

See also

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA005277(Nontotients)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 134 - 135
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA045575(Nonnegative numbers of the form x^y - y^x, for x,y > 1)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA007749(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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