| Divisibility-based sets of integers |
| Forms of factorization: |
| Prime number |
| Composite number |
| Powerful number |
| Square-free number |
| Achilles number |
| Constrained divisor sums: |
| Perfect number |
| Almost perfect number |
| Quasiperfect number |
| Multiply perfect number |
| Hyperperfect number |
| Superperfect number |
| Unitary perfect number |
| Semiperfect number |
| Primitive semiperfect number |
| Practical number |
| Numbers with many divisors: |
| Abundant number |
| Highly abundant number |
| Superabundant number |
| Colossally abundant number |
| Highly composite number |
| Superior highly composite number |
| Other: |
| Untouchable number |
| Deficient number |
| Weird number |
| Amicable number |
| Friendly number |
| Sociable number |
| Solitary number |
| Sublime number |
| Harmonic divisor number |
| Frugal number |
| Equidigital number |
| Extravagant number |
| See also: |
| Divisor function |
| Divisor |
| Prime factor |
| Factorization |
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
References
- R.G.E. Pinch (1998), Economical Numbers.
- Chris Caldwell, The Prime Glossary: extravagant number at The Prime Pages.
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