A050355 Ordered factorizations with one level of parentheses indexed by prime signatures. A050354(A025487).
1, 1, 3, 5, 9, 21, 27, 81, 37, 81, 111, 297, 201, 243, 513, 1053, 945, 729, 2187, 1317, 3645, 365, 2745, 4077, 2187, 8829, 7209, 12393, 2433, 13257, 16605, 6561, 34263, 35397, 41553, 13473, 59697, 10155, 64881, 19683, 44793, 129033, 18993, 71307
Offset: 1