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 A321451 #11 Nov 11 2018 18:27:26
%S A321451 1,1,1,2,2,6,4,14,8,20,16,55,22,100,45,108,64,296,93,489,145,447,241,
%T A321451 1254,284,1692,487,1492,627,4564,811,6841,1172,4531,1744,12260,1970,
%U A321451 21636,3103,12193,3719,44582,4645,63260,6417,29947,8987,124753,9784,162107,14247
%N A321451 Number of integer partitions of n that cannot be partitioned into two or more blocks with equal sums.
%F A321451 a(n) = A000041(n) - A321452(n).
%e A321451 The a(1) = 1 through a(9) = 20 partitions:
%e A321451 (1) (2) (3) (4) (5) (6) (7) (8) (9)
%e A321451 (21) (31) (32) (42) (43) (53) (54)
%e A321451 (41) (51) (52) (62) (63)
%e A321451 (221) (411) (61) (71) (72)
%e A321451 (311) (322) (332) (81)
%e A321451 (2111) (331) (521) (432)
%e A321451 (421) (611) (441)
%e A321451 (511) (5111) (522)
%e A321451 (2221) (531)
%e A321451 (3211) (621)
%e A321451 (4111) (711)
%e A321451 (22111) (3222)
%e A321451 (31111) (4221)
%e A321451 (211111) (4311)
%e A321451 (5211)
%e A321451 (6111)
%e A321451 (22221)
%e A321451 (42111)
%e A321451 (51111)
%e A321451 (411111)
%e A321451 A complete list of all multiset partitions of the partition (2111) into two or more blocks is: ((1)(112)), ((2)(111)), ((11)(12)), ((1)(1)(12)), ((1)(2)(11)), ((1)(1)(1)(2)). None of these has equal block-sums, so (2111) is counted toward a(5).
%e A321451 On the other hand, the partition (321) can be partitioned as ((12)(3)), which has two or more blocks and equal block-sums, so (321) is not counted toward a(6).
%t A321451 hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]*k]];
%t A321451 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A321451 Table[Length[Select[IntegerPartitions[n],Length[Select[facs[Times@@Prime/@#],SameQ@@hwt/@#&]]==1&]],{n,10}]
%Y A321451 Cf. A000041, A265947, A276024, A279787, A305551, A306017, A317141, A320322, A321452, A321453, A321454, A321455.
%K A321451 nonn
%O A321451 0,4
%A A321451 _Gus Wiseman_, Nov 10 2018
%E A321451 a(33)-a(50) from _Alois P. Heinz_, Nov 11 2018