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 A320322 #5 Oct 11 2018 10:09:55
%S A320322 1,0,0,0,2,2,5,5,9,11,18,19,28,30,42,50,68,76,102,113,146,170,212,241,
%T A320322 312,356,441,514,628,720,887,1008,1215,1403,1660,1903,2291,2609,3107,
%U A320322 3594,4254,4864,5739,6546,7672,8811,10237,11651,13583,15420,17867,20382
%N A320322 Number of integer partitions of n whose product is a perfect power.
%e A320322 The a(4) = 2 through a(11) = 19 integer partitions:
%e A320322 4 41 33 331 8 9 55 551
%e A320322 22 221 42 421 44 81 82 632
%e A320322 222 2221 422 333 91 821
%e A320322 411 4111 2222 441 433 911
%e A320322 2211 22111 3311 4221 442 4331
%e A320322 4211 22221 811 4421
%e A320322 22211 33111 3322 8111
%e A320322 41111 42111 3331 33221
%e A320322 221111 222111 4222 33311
%e A320322 411111 4411 42221
%e A320322 2211111 22222 44111
%e A320322 42211 222221
%e A320322 222211 422111
%e A320322 331111 2222111
%e A320322 421111 3311111
%e A320322 2221111 4211111
%e A320322 4111111 22211111
%e A320322 22111111 41111111
%e A320322 221111111
%t A320322 Table[Length[Select[IntegerPartitions[n],GCD@@FactorInteger[Times@@#][[All,2]]>1&]],{n,30}]
%Y A320322 Cf. A003963, A064573, A305551, A319056, A319066, A319071, A319169, A320325.
%K A320322 nonn
%O A320322 0,5
%A A320322 _Gus Wiseman_, Oct 10 2018