A362426 Number of compositions (ordered partitions) of n into 2 perfect powers (A001597).

0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 2, 0, 2, 2, 0, 0, 1, 4, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1, 4, 2, 2, 4, 2, 0, 0, 4, 4, 0, 2, 2, 2, 0, 0, 2, 0, 3, 0, 4, 2, 1, 0, 0, 4, 2, 2, 0, 2, 0, 2, 1, 4, 0, 0, 4, 0, 0, 0, 3, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 4, 0, 0, 0, 4, 2, 2

Offset: 0

Author

Ilya Gutkovskiy, Apr 19 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A001597.

Programs

Mathematica

perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[;; , 2]] > 1; a[n_] := Total[Multinomial @@ Tally[#][[;; , 2]] & /@ Select[IntegerPartitions[n, {2}], AllTrue[#, perfectPowerQ] &]]; Array[a, 100, 0] (* Amiram Eldar, May 05 2023 *)