Frugal number
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). For example, in base 10, 125 = 5, 128 = 2, 243 = 3, and 256 = 2 are frugal numbers . The first frugal number which is not a prime power is 1029 = 3 × 7. In base 2, thirty-two is a frugal number, since 32 = 2 is written in base 2 as 100000 = 10. The term economical number  has been used about a frugal number, but also about a number which is either frugal or equidigital. Mathematical definition. Let formula_1 be a number base, and let formula_2 be the number of digits in a natural number formula_3 for base formula_4. A natural number formula_3 has the integer factorisation and is an frugal number in base formula_4 if where formula_9 is the p-adic valuation of formula_3.