Extravagant number

An extravagant number (also known as a wasteful number) is a natural number that has fewer digits than the number of digits in its prime factorization (including exponents). For example, in base-10 arithmetic 4 = 2², 6 = 2×3, 8 = 2³, and 9 = 3² are extravagant numbers.

Extravagant numbers can be defined in any base. There are infinitely many extravagant numbers, no matter what base is used.

See also

* Equidigital number

* Frugal number

References

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

Chris Caldwell, The Prime Glossary: extravagant number at The Prime Pages.

Number Theory