A362425 Number of partitions of n into 3 distinct perfect powers (A001597).

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

Offset

0,22

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_] := Count[IntegerPartitions[n, {3}], _?(AllTrue[#, perfectPowerQ] && UnsameQ @@ # &)]; Array[a, 100, 0] (* Amiram Eldar, May 05 2023 *)

Crossrefs

Cf. A001597, A362424.

Sequence in context: A030216 A357352 A339376 * A159459 A304095 A276675

Adjacent sequences: A362422 A362423 A362424 * A362426 A362427 A362428

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 19 2023

Status

approved