A frugal number is a natural number

Natural number

In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 that has more digits

Numerical digit

A digit is a symbol used in combinations to represent numbers in positional numeral systems. The name "digit" comes from the fact that the 10 digits of the hands correspond to the 10 symbols of the common base 10 number system, i.e...

 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

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

Equidigital number

An equidigital number is a number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. For example, in base-10 arithmetic 1, 2, 3, 5, 7, and 10 are equidigital numbers...

.