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 = 53, 128 = 27, 243 = 35, and 256 = 28 are frugal numbers. 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.

Mathematical definition
Let $$b > 1$$ be a number base, and let $$K_b(n) = \lfloor \log_b{n} \rfloor + 1$$ be the number of digits in a natural number $$n$$ for base $$b$$. A natural number $$n$$ has the prime factorisation
 * $$n = \prod_{\stackrel{p \,\mid\, n}{p\text{ prime}}} p^{v_p(n)}$$

where $$v_p(n)$$ is the p-adic valuation of $$n$$, and $$n$$ is an frugal number in base $$b$$ if
 * $$K_b(n) > \sum_ K_b(p) + \sum_ K_b(v_p(n)).$$