Infinitary Perfect Number

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, ... (OEIS A007357). Cohen (1990) found 14 such numbers, and 155 are known as of January 2004 (Pedersen).

REFERENCES:

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." https://amicable.adsl.dk/aliquot/infper.txt.

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