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 A353426 #10 May 20 2022 08:51:22
%S A353426 1,1,1,1,2,1,2,1,1,2,2,1,2,2,3,3,5,4,6,5,6,6,7,8,10,12,12,14,13,13,18,
%T A353426 15,16,19,20,20,32,37,53,74,105
%N A353426 Number of integer partitions of n that are empty or a singleton or whose multiplicities are a sub-multiset that is already counted.
%C A353426 a(n) is number of integer partitions of n whose Heinz number belongs to A353393, where the Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A353426 The a(n) partitions for selected n (A..M = 10..22):
%e A353426 n=1: n=4: n=14: n=16: n=17: n=18: n=22:
%e A353426 ------------------------------------------------------------------
%e A353426 (1) (4) (E) (G) (H) (I) (M)
%e A353426 (22) (5522) (4444) (652211) (7722) (9922)
%e A353426 (532211) (6622) (742211) (752211) (972211)
%e A353426 (642211) (832211) (842211) (A62211)
%e A353426 (732211) (932211) (B52211)
%e A353426 (333222111) (C42211)
%e A353426 (D32211)
%t A353426 oosQ[y_]:=Length[y]<=1||MemberQ[Subsets[Sort[y],{Length[Union[y]]}],Sort[Length/@Split[y]]]&&oosQ[Sort[Length/@Split[y]]];
%t A353426 Table[Length[Select[IntegerPartitions[n],oosQ]],{n,0,30}]
%Y A353426 The non-recursive version is A325702, ranked by A325755.
%Y A353426 The version for compositions is A353391, non-recursive A353390.
%Y A353426 These partitions are ranked by A353393, nonprime A353389.
%Y A353426 A047966 counts uniform partitions, compositions A329738.
%Y A353426 A239455 counts Look-and-Say partitions, ranked by A351294.
%Y A353426 Cf. A000041, A002033, A074761, A181819, A181821, A323014, A325534, A333755.
%K A353426 nonn,more
%O A353426 0,5
%A A353426 _Gus Wiseman_, May 16 2022