Dunno if this will help or not but:

Every multiple of a semiperfect number is semiperfect, as are all numbers:
(2^m)p for m >= 1 and p, a prime between 2^m and 2^(m+1). (Guy 1994, p. 47).

Biblio: Guy, R. K. "Almost Perfect, Quasi-Perfect, Pseudoperfect, Harmonic, Weird, Multiperfect and Hyperperfect Numbers." §B2 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 45-53, 1994.