A050119 a(n)=b(n)-b(n-1), where b=A050118 (ordered products of Lucas numbers).

1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 3, 1, 6, 1, 4, 3, 8, 3, 2, 5, 4, 14, 4, 1, 10, 7, 22, 5, 2, 3, 15, 11, 36, 10, 1, 4, 25, 18, 58, 15, 3, 2, 5, 40, 29, 94, 25, 4, 1, 10, 65, 47, 152, 40, 5, 2, 3, 15, 105, 76, 246, 65, 10, 1, 4, 25, 170, 123