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Infinary Perfect Number

Let $\sigma_\infty(n)$ be the Sum of the Infinary Divisors of a number $n$. An infinary perfect number is a number $n$ such that $\sigma_\infty(n)=2n$. Cohen (1990) found 14 such numbers. The first few are 6, 60, 90, 36720, ... (Sloane's A007357).

See also Infinary Multiperfect Number


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

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

Sloane, N. J. A. Sequence A007357/M4267 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

© 1996-9 Eric W. Weisstein