Let be the sum of the infinitary divisors of a number . An infinitary perfect number is a number such that . The first few are 6, 60, 90, 36720, ... (Sloane's A007357). Cohen (1990) found 14 such numbers, and 155 are known as of January 2004 (Pedersen).

Cohen, G. L. "On an Integer's Infinitary Divisors." Math. Comput. 54, 395-411, 1990.

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 54, 1994.

Pedersen, J. M. "Tables of Aliquot Cycles." http://amicable.adsl.dk/aliquot/infper.txt.

Sloane, N. J. A. Sequence A007357/M4267 in "The On-Line Encyclopedia of Integer Sequences."

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Weisstein, Eric W. "Infinitary Perfect Number." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/InfinitaryPerfectNumber.html