A339555 Number of subsets of {2..n} such that the product of the elements is a perfect power.
1, 1, 1, 1, 3, 3, 5, 5, 11, 25, 41, 41, 80, 80, 144, 284, 568, 568, 1147, 1147, 2339, 4667, 8763, 8763, 17548, 35196, 67964, 135918, 273806, 273806, 548956, 548956, 1097974, 2194294, 4291446, 8608698, 17216783, 17216783, 33993999, 67979983, 135956742
Offset: 0
Keywords
Examples
a(8) = 11 subsets: {}, {4}, {8}, {2, 4}, {2, 8}, {4, 8}, {2, 3, 6}, {2, 4, 8}, {3, 6, 8}, {2, 3, 4, 6} and {3, 4, 6, 8}.
Links
- Eric Weisstein's World of Mathematics, Perfect Power
Formula
a(p) = a(p-1) for p prime.
Extensions
a(25)-a(40) from Alois P. Heinz, Dec 08 2020