118 (number)

From Wikipedia, the free encyclopedia
(Redirected from One hundred eighteen)
Jump to navigation Jump to search
← 117 118 119 →
Cardinalone hundred eighteen
Ordinal118th
(one hundred eighteenth)
Factorization2 × 59
Divisors1, 2, 59, 118
Greek numeralΡΙΗ´
Roman numeralCXVIII
Binary11101102
Ternary111013
Senary3146
Octal1668
Duodecimal9A12
Hexadecimal7616

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

In mathematics[edit]

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[edit]

References[edit]

  1. ^ Sloane, N. J. A. (ed.). "Sequence A005277 (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.). "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. ^ 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.