118 (one hundred
ndeighteen) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
117 and preceding
119.
In mathematics
There is no answer to the equation
φ(''x'') = 118, making 118 a
nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie ...
.
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
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
, where !! denotes the
double factorial
In mathematics, the double factorial of a number , denoted by , is the product of all the positive integers up to that have the same Parity (mathematics), parity (odd or even) as . That is,
n!! = \prod_^ (n-2k) = n (n-2) (n-4) \cdots.
Restated ...
(the product of even integers up to 118).
See also
*
118 (disambiguation)
References
Integers
{{Num-stub