Equidigital number

An equidigital number is a number that has the same number of digits as the number of digits in its prime factorization, including exponents but excluding exponents equal to 1. For example, in base-10 arithmetic 1, 2, 3, 5, 7, and 10 (2×5) are equidigital numbers. All prime numbers are equidigital numbers in any base.

A number that is either equidigital or frugal is said to be economical.

See also

• Extravagant number
• Frugal number

References

• R.G.E. Pinch (1998), Economical Numbers.

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