In number theory, a frugal number is a natural number in a given number base that has more digits than the number of digits in its prime factorization in the given number base (including exponents).
[1] For example, in base 10, 125 = 53, 128 = 27, 243 = 35, and 256 = 28 are frugal numbers (sequence A046759 in the OEIS).
The first frugal number which is not a prime power is 1029 = 3 × 73.
In base 2, thirty-two is a frugal number, since 32 = 25 is written in base 2 as 100000 = 10101.
The term economical number has been used for a frugal number, but also for a number which is either frugal or equidigital.
A natural number
has the prime factorisation where
is an frugal number in base