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 A321452 #14 Nov 12 2018 15:27:47
%S A321452 0,0,1,1,3,1,7,1,14,10,26,1,55,1,90,68,167,1,292,1,482,345,761,1,1291,
%T A321452 266,1949,1518,3091,1,4793,1,7177,5612,10566,2623,16007,1,22912,18992,
%U A321452 33619,1,48529,1,68758,59187,96571,1,137489,11418,189979,167502,264299
%N A321452 Number of integer partitions of n that can be partitioned into two or more blocks with equal sums.
%C A321452 a(n) = 1 if and only if n is prime. - _Chai Wah Wu_, Nov 12 2018
%F A321452 a(n) = A000041(n) - A321451(n).
%e A321452 The a(2) = 1 through a(9) = 10 partitions:
%e A321452 (11) (111) (22) (11111) (33) (1111111) (44) (333)
%e A321452 (211) (222) (422) (3321)
%e A321452 (1111) (321) (431) (32211)
%e A321452 (2211) (2222) (33111)
%e A321452 (3111) (3221) (222111)
%e A321452 (21111) (3311) (321111)
%e A321452 (111111) (4211) (2211111)
%e A321452 (22211) (3111111)
%e A321452 (32111) (21111111)
%e A321452 (41111) (111111111)
%e A321452 (221111)
%e A321452 (311111)
%e A321452 (2111111)
%e A321452 (11111111)
%e A321452 The partition (32111) can be partitioned as ((13)(112)), and the blocks both sum to 4, so (32111) is counted under a(8).
%t A321452 hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]];
%t A321452 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A321452 Table[Length[Select[IntegerPartitions[n],Length[Select[facs[Times@@Prime/@#],SameQ@@hwt/@#&]]>1&]],{n,10}]
%Y A321452 Cf. A000041, A265947, A276024, A279787, A305551, A306017, A317141, A320322, A321451, A321453, A321454, A321455.
%K A321452 nonn
%O A321452 0,5
%A A321452 _Gus Wiseman_, Nov 10 2018
%E A321452 a(26)-a(52) from _Alois P. Heinz_, Nov 11 2018