A frugal (or economical) number uses fewer digits to write its prime factorization — primes and exponents included — than to write the number itself. For example, \(125\) takes three digits, but its factorization \(5^3\) takes only two ("5" and "3"); \(1024 = 2^{10}\) writes as three digits versus four. The first frugal numbers are 125, 128, 243, 256, 343, 512, 625, 729, 1024.
Frugal numbers contrast with equidigital numbers (factorization the same length) and extravagant/wasteful numbers (factorization longer). Whether there are infinitely many frugal numbers is known to depend on the distribution of prime powers; under standard conjectures, there are.