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.

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

See also

• Equidigital number
• Frugal number

Notes

References

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

Divisibility-based sets of integers Overview Integer factorization Divisor Unitary divisor Divisor function Prime factor Fundamental theorem of arithmetic Arithmetic number Factorization forms Prime Composite Semiprime Pronic Sphenic Square-free Powerful Perfect power Achilles Smooth Regular Rough Unusual Constrained divisor sums Perfect Almost perfect Quasiperfect Multiply perfect Hemiperfect Hyperperfect Superperfect Unitary perfect Semiperfect Practical Erdős–Nicolas With many divisors Abundant Primitive abundant Highly abundant Superabundant Colossally abundant Highly composite Superior highly composite Weird Aliquot sequence-related Untouchable Amicable Sociable Betrothed Other sets Deficient Friendly Solitary Sublime Harmonic divisor Frugal Equidigital Extravagant