Extravagant number

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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).[1] For example, in base-10 arithmetic 4 = 2², 6 = 2×3, 8 = 2³, and 9 = 3² are extravagant numbers (sequence A046760 in the OEIS).

Extravagant numbers can be defined in any base. There are infinitely many extravagant numbers, no matter what base is used.[1]

See also

Notes

  1. ^ a b Darling, David J. (2004). The universal book of mathematics: from Abracadabra to Zeno's paradoxes. John Wiley & Sons. p. 102. ISBN 978-0-471-27047-8.

References

  • R.G.E. Pinch (1998), Economical Numbers.
  • Chris Caldwell, The Prime Glossary: extravagant number at The Prime Pages.


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