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 A370806 #13 Feb 14 2025 11:15:47
%S A370806 0,0,0,0,1,0,1,1,3,2,4,4,8,9,11,14,19,24,29,39,47,58,70,85,104,129,
%T A370806 152,184,223,264,313,374,442,524,617,719,852,993,1159,1344,1579,1817,
%U A370806 2114,2440,2826,3250,3750,4297,4944,5662,6475,7404,8462,9634,10972,12480
%N A370806 Number of non-strict condensed integer partitions of n.
%C A370806 These are non-strict partitions such that it is possible to choose a different divisor of each part.
%e A370806 The a(4) = 1 through a(13) = 9 partitions:
%e A370806 (22) . (33) (322) (44) (441) (55) (443) (66) (544)
%e A370806 (332) (522) (433) (533) (444) (553)
%e A370806 (422) (442) (722) (552) (661)
%e A370806 (622) (4322) (633) (733)
%e A370806 (822) (922)
%e A370806 (4332) (4432)
%e A370806 (4431) (5332)
%e A370806 (5322) (5422)
%e A370806 (6322)
%t A370806 Table[Length[Select[IntegerPartitions[n],!UnsameQ@@# && Length[Select[Tuples[Divisors/@#],UnsameQ@@#&]]>0&]],{n,0,30}]
%Y A370806 This is the non-strict case of A239312, complement A370320.
%Y A370806 These partitions have as ranks the nonsquarefree terms of A368110.
%Y A370806 A000005 counts divisors.
%Y A370806 A000041 counts integer partitions, strict A000009.
%Y A370806 A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A370806 A370592 counts factor-choosable partitions, complement A370593.
%Y A370806 A370814 counts condensed factorizations, complement A370813.
%Y A370806 Cf. A355739, A355740, A370595, A370804, A370808, A370810.
%K A370806 nonn
%O A370806 0,9
%A A370806 _Gus Wiseman_, Mar 04 2024
%E A370806 More terms from _Jinyuan Wang_, Feb 14 2025