Infinary Multiperfect Number
Let 
be the Sum of the Infinary Divisors of a number 
.An infinary 
-multiperfect number is a number such that 
. Cohen (1990) found 13 infinary 3-multiperfects, seven 4-multiperfects, and two 5-multiperfects.
References
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.
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