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%I #5 Dec 31 2018 13:18:47
%S 1,1,2,3,5,6,10,11,15,17,23,24,33,34,42,46,56,57,71,72,88,93,109,110,
%T 134,136,158,163,191,192,229,230,266,273,311,315,370,371,419,428,491,
%U 492,565,566,642,654,730,731,836,838,936
%N Number of integer partitions of n whose parts are all powers of the same squarefree number.
%C First differs from A072720 at a(12) = 33, A072720(12) = 34.
%e The a(1) = 1 through a(8) = 15 integer partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8)
%e (11) (21) (22) (41) (33) (61) (44)
%e (111) (31) (221) (42) (331) (71)
%e (211) (311) (51) (421) (422)
%e (1111) (2111) (222) (511) (611)
%e (11111) (411) (2221) (2222)
%e (2211) (4111) (3311)
%e (3111) (22111) (4211)
%e (21111) (31111) (5111)
%e (111111) (211111) (22211)
%e (1111111) (41111)
%e (221111)
%e (311111)
%e (2111111)
%e (11111111)
%t radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All,2]]);
%t powsqfQ[n_]:=SameQ@@Last/@FactorInteger[n];
%t Table[Length[Select[IntegerPartitions[n],And[And@@powsqfQ/@#,SameQ@@radbase/@DeleteCases[#,1]]&]],{n,30}]
%Y Cf. A000961, A005117, A018819, A023893, A052410, A072720, A072721, A072774, A302593, A322847, A322900, A322901, A322911.
%K nonn
%O 0,3
%A _Gus Wiseman_, Dec 30 2018
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