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 A330216 #5 Dec 06 2019 09:36:44
%S A330216 0,0,0,0,1,1,1,1,1,2,2,2,3,4,3,4,5,7,8,8,10,12,12,15,18,19,20,24,25,
%T A330216 28,38,41,43,50,55,63,79,85,88,104,116,124,143,157,173,197,214,235,
%U A330216 274,294,319,363,393,430,487,529,577,647,692,752,856,925,992,1099
%N A330216 Number of strict integer partitions of n whose product is a powerful number.
%e A330216 The a(n) partitions for n = 4, 9, 12, 13, 16, 17, 18:
%e A330216 (4) (9) (8,4) (9,4) (16) (9,8) (12,6)
%e A330216 (8,1) (9,3) (6,4,3) (9,4,3) (16,1) (16,2)
%e A330216 (6,3,2,1) (8,4,1) (12,3,1) (8,6,3) (9,8,1)
%e A330216 (9,3,1) (9,4,2,1) (9,6,2) (8,6,3,1)
%e A330216 (6,4,3,2,1) (10,5,2) (9,4,3,2)
%e A330216 (12,3,2) (9,6,2,1)
%e A330216 (9,4,3,1) (10,5,2,1)
%e A330216 (12,3,2,1)
%t A330216 powQ[n_]:=Min@@Last/@FactorInteger[n]>1;
%t A330216 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&powQ[Times@@#]&]],{n,0,30}]
%Y A330216 The non-strict version is A330106.
%Y A330216 Powerful numbers are A001694.
%Y A330216 Partitions whose product is a perfect power are A320322.
%Y A330216 Cf. A000009, A045778, A001597, A003963, A064573, A320325.
%K A330216 nonn
%O A330216 0,10
%A A330216 _Gus Wiseman_, Dec 05 2019