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 A319071 #21 Oct 11 2018 10:09:41
%S A319071 1,0,0,0,2,0,2,0,3,2,3,0,4,1,4,3,7,1,7,1,8,6,8,0,15,5,12,6,15,4,22,4,
%T A319071 24,12,22,8,35,7,30,16,42,9,50,9,50,30,53,7,79,22,72,33,87,21,109,26,
%U A319071 111,55,117,24,168,40,149,65,178,59
%N A319071 Number of integer partitions of n whose product of parts is a perfect power and whose parts all have the same number of prime factors, counted with multiplicity.
%C A319071 The positions of zeros appear to be A048278.
%e A319071 The a(4) = 2 through a(16) = 7 integer partitions (G = 16):
%e A319071 4 33 8 9 55 66 94 77 555 G
%e A319071 22 222 44 333 3322 444 5522 33333 88
%e A319071 2222 22222 3333 332222 333222 664
%e A319071 222222 2222222 4444
%e A319071 5533
%e A319071 333322
%e A319071 22222222
%t A319071 Table[Length[Select[IntegerPartitions[n],And[GCD@@FactorInteger[Times@@#][[All,2]]>1,SameQ@@PrimeOmega/@#]&]],{n,30}]
%Y A319071 Cf. A003963, A048278, A064573, A279787, A305551, A319056, A319066, A319169, A320322, A320323.
%K A319071 nonn
%O A319071 0,5
%A A319071 _Gus Wiseman_, Oct 10 2018