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

0,6

Links

Table of n, a(n) for n=0..91.

Eric Weisstein's World of Mathematics, Perfect Power.

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 *)

Crossrefs

Cf. A001597.

Sequence in context: A325406 A360675 A257900 * A039971 A205593 A277937

Adjacent sequences: A362423 A362424 A362425 * A362427 A362428 A362429

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 19 2023

Status

approved