Frugal number
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| Divisibility-based sets of integers |
| Form 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: |
| 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 |
A frugal number is a natural number that has more digits than the number of digits in its prime factorization (including exponents). For example, using base-10 arithmetic, the first few frugal numbers are 125 (53), 128 (27), 243 (35), and 256 (28). Frugal numbers also exist in other bases; for instance, in binary arithmetic thirty-two is a frugal number, since 10101 = 100000.
The base-10 frugal numbers up to 2000 are:
- 125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875 (sequence A046759 in OEIS)
The term economical number has been used about a frugal number, but also about a number which is either frugal or equidigital.
[edit] See also
[edit] References
- R.G.E. Pinch (1998), Economical Numbers
