Infinary Multiperfect Number

Let $\sigma_\infty(n)$ be the Sum of the Infinary Divisors of a number $n$. An infinary $k$-multiperfect number is a number $n$ such that $\sigma_\infty(n)=kn$. Cohen (1990) found 13 infinary 3-multiperfects, seven 4-multiperfects, and two 5-multiperfects.

See also Infinary Perfect Number

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.