A362427 Number of compositions (ordered partitions) of n into perfect powers > 1.

1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 3, 2, 0, 0, 6, 5, 1, 0, 10, 10, 3, 0, 18, 23, 9, 2, 31, 46, 22, 6, 56, 94, 56, 19, 102, 184, 129, 50, 187, 364, 293, 134, 349, 710, 638, 332, 661, 1384, 1375, 805, 1287, 2683, 2904, 1878, 2547, 5205, 6069, 4306, 5150, 10115, 12530, 9659, 10558

Offset: 0

Author

Ilya Gutkovskiy, Apr 19 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Perfect Power.

Crossrefs

Cf. A001597, A112344, A112345.

Programs

Mathematica

perfectPowerQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; a[n_] := Total[Multinomial @@ Tally[#][[;; , 2]] & /@ Select[IntegerPartitions[n], AllTrue[#, perfectPowerQ] &]]; Array[a, 50, 0] (* Amiram Eldar, May 05 2023 *)

Formula

G.f.: 1 / (1 - Sum_{k>=2} x^A001597(k)).