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# 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)

Related:

FrugalNumber, EquidigitalNumber

Synonym:

wasteful number

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

11A63*no label found*

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