Equidigital number

Demonstration, with Cuisenaire rods, that the composite number 10 is equidigital: 10 has two digits, and 2×5 has two digits (1 is excluded)

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 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