Infinitary Perfect Number

Let sigma_infty(n) be the sum of the infinitary divisors of a number n. An infinitary perfect number is a number n such that sigma_infty(n)=2n. The first few are 6, 60, 90, 36720, ... (OEIS A007357). Cohen (1990) found 14 such numbers, and 155 are known as of January 2004 (Pedersen).

See also

Infinitary Divisor, Infinitary Multiperfect Number

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

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Infinitary Perfect Number

Cite this as:

Weisstein, Eric W. "Infinitary Perfect Number." From MathWorld--A Wolfram Web Resource.

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