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

0,5

Links

Table of n, a(n) for n=0..40.

Eric Weisstein's World of Mathematics, Perfect Power

Formula

a(p) = a(p-1) for p prime.

Example

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}.

Crossrefs

Cf. A001597, A089819, A320322, A339554.

Sequence in context: A146245 A245144 A279021 * A213029 A348843 A290208

Adjacent sequences: A339552 A339553 A339554 * A339556 A339557 A339558

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 08 2020

Extensions

a(25)-a(40) from Alois P. Heinz, Dec 08 2020

Status

approved