Numbers which are not perfect and for which
or equivalently
where divisor function . Deficient numbers are
sometimes called defective numbers (Singh 1997). Primes ,
prime powers , and any divisors of a perfect
or deficient number are all deficient. The first few deficient numbers are 1, 2,
3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, ... (OEIS A005100 ).
See also Abundant Number ,
Almost
Perfect Number ,
Perfect Number
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References Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. Guy, R. K. Unsolved
Problems in Number Theory, 2nd ed. Singh, S. Fermat's
Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. Sloane, N. J. A. Sequence
A005100 /M0514 in "The On-Line Encyclopedia
of Integer Sequences." Souissi, M. Un Texte Manuscrit d'Ibn Al-Bannā'
Al-Marrakusi sur les Nombres Parfaits, Abondants, Deficients, et Amiables. Karachi,
Pakistan: Hamdard Nat. Found., 1975. Referenced on Wolfram|Alpha Deficient Number
Cite this as:
Weisstein, Eric W. "Deficient Number."
From MathWorld https://mathworld.wolfram.com/DeficientNumber.html
Subject classifications
is the divisor function. Deficient numbers are
sometimes called defective numbers (Singh 1997). Primes,
prime powers, and any divisors of a perfect
or deficient number are all deficient. The first few deficient numbers are 1, 2,
3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, ... (OEIS A005100).
