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
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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.

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