A number
is called wasteful if the number of digits in the prime factorization of (including powers) uses more digits than the number of digits
in .
The first few wasteful numbers are 4, 6, 8, 9, 12, 18, 20, 22, 24 ... (OEIS A046760).
A number that is not wasteful is called a frugal number
(Pinch).