In number theory, an extravagant number (also known as a wasteful number) is a natural number in a given number base that has fewer digits than the number of digits in its prime factorization in the given number base (including exponents).
[1] For example, in base 10, 4 = 22, 6 = 2×3, 8 = 23, and 9 = 32 are extravagant numbers (sequence A046760 in the OEIS).
There are infinitely many extravagant numbers in every base.
be a number base, and let
A natural number
has the prime factorisation where
is the p-adic valuation of
is an extravagant number in base