A050360 Abelian groups (factorizations into prime powers >1) indexed by prime signatures. A000688(A025487).

1, 1, 2, 1, 3, 2, 5, 3, 1, 7, 4, 5, 2, 11, 6, 7, 3, 15, 10, 4, 11, 1, 9, 5, 22, 14, 6, 15, 2, 15, 7, 30, 22, 10, 22, 3, 21, 8, 11, 42, 9, 30, 4, 25, 14, 30, 5, 33, 12, 15, 56, 15, 44, 1, 6, 35, 22, 42, 7, 45, 20, 22, 77, 21, 60, 2, 10, 55, 18, 30, 56, 8, 25, 11, 66, 28, 9, 30, 49, 101