Deficient Number

Numbers which are not perfect and for which

or equivalently

where  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).

REFERENCES:

Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Dover, pp. 3-33, 2005.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 45, 1994.

Singh, S. Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. New York: Walker, p. 11, 1997.

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.