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118 (number)

FieldValue
number118
divisor1, 2, 59, 118

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

In mathematics

There is no solution to the equation φ(x) = 118, making 118 a nontotient.

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.

Because of its expression as , it is a Leyland number of the second kind.

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

In chemistry

, 118 elements have an official name assigned by IUPAC, the last of which (number 118) being oganesson.

References

References

  1. {{cite OEIS. A005277. Nontotients
  2. Wells, D. ''[[The Penguin Dictionary of Curious and Interesting Numbers]]'' London: Penguin Group. (1987): 134 - 135
  3. {{cite OEIS. A045575. Nonnegative numbers of the form x^y - y^x, for x,y > 1
  4. {{cite OEIS. A007749. Numbers k such that k!! - 1 is prime
  5. (30 November 2016). "IUPAC Announces the Names of the Elements 113, 115, 117, and 118". [[IUPAC]].
  6. St. Fleur, Nicholas. (1 December 2016). "Four New Names Officially Added to the Periodic Table of Elements". [[The New York Times]].
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