# extravagant number

An extravagant number or wasteful number $n$ is an integer with a base $b$ representation of $k$ digits for which the prime factorization uses more than $k$ digits (with repeated prime factors grouped with exponents and the digits of those exponents counted whenever greater than 1). The first few extravagant numbers in base 10 are 4, 6, 8, 9, 12, 18, 20, 22, 24, 26, 28, 30, 33, 34, 36, 38, 39, 40, 42, 44, 45, 46, 48, etc. (listed in A046760 of Sloane’s OEIS).

## References

• 1 D. Darling, “Economical number” in The Universal Book of Mathematics: From Abracadabra To Zeno’s paradoxes. Hoboken, New Jersey: Wiley (2004)
Title extravagant number ExtravagantNumber 2013-03-22 16:41:20 2013-03-22 16:41:20 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11A63 wasteful number FrugalNumber EquidigitalNumber