Frugal number

A frugal number is a natural number that has more digits than the number of digits in its prime factorization (including exponents). For example, using base-10 arithmetic, the first few frugal numbers are 125 (5³), 128 (2⁷), 243 (3⁵), and 256 (2⁸). Frugal numbers also exist in other bases; for instance, in binary arithmetic thirty-two is a frugal number, since 10¹⁰¹ = 100000.

The base-10 frugal numbers up to 2000 are:

125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875 (sequence A046759 in OEIS)

The term economical number has been used about a frugal number, but also about a number which is either frugal or equidigital.

See also

• Equidigital number
• Extravagant number

References

• R.G.E. Pinch (1998), Economical Numbers