This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A330106 #5 Dec 06 2019 09:35:50
%S A330106 0,0,0,0,2,2,5,5,9,11,18,19,30,36,51,62,87,104,141,171,225,271,349,
%T A330106 419,534,643,804,965,1197,1431,1766,2106,2571,3063,3719,4410,5325,
%U A330106 6305,7567,8939,10678,12572,14961,17567,20804,24389,28775,33626,39551,46106
%N A330106 Number of integer partitions of n whose product is a powerful number.
%e A330106 The a(4) = 2 through a(10) = 18 partitions:
%e A330106 (4) (41) (33) (331) (8) (9) (55)
%e A330106 (22) (221) (42) (421) (44) (81) (82)
%e A330106 (222) (2221) (422) (333) (91)
%e A330106 (411) (4111) (2222) (441) (433)
%e A330106 (2211) (22111) (3311) (4221) (442)
%e A330106 (4211) (22221) (811)
%e A330106 (22211) (33111) (3322)
%e A330106 (41111) (42111) (3331)
%e A330106 (221111) (222111) (4222)
%e A330106 (411111) (4411)
%e A330106 (2211111) (22222)
%e A330106 (42211)
%e A330106 (222211)
%e A330106 (331111)
%e A330106 (421111)
%e A330106 (2221111)
%e A330106 (4111111)
%e A330106 (22111111)
%t A330106 powQ[n_]:=Min@@Last/@FactorInteger[n]>1;
%t A330106 Table[Length[Select[IntegerPartitions[n],powQ[Times@@#]&]],{n,0,30}]
%Y A330106 The strict version is A330216.
%Y A330106 Powerful numbers are A001694.
%Y A330106 Partitions whose product is a perfect power are A320322.
%Y A330106 Cf. A000041, A001055, A001597, A003963, A064573, A320325.
%K A330106 nonn
%O A330106 0,5
%A A330106 _Gus Wiseman_, Dec 05 2019