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 A370807 #5 Mar 04 2024 23:31:40
%S A370807 0,0,0,0,1,0,3,1,4,4,8,9,15,17,25,30,43,54,72,87,115,139,181,224,283,
%T A370807 342,429,519,647,779,967
%N A370807 Number of integer partitions of n into parts > 1 such that it is not possible to choose a different prime factor of each part.
%e A370807 The a(0) = 0 through a(11) = 9 partitions:
%e A370807 . . . . (22) . (33) (322) (44) (333) (55) (443)
%e A370807 (42) (332) (432) (82) (533)
%e A370807 (222) (422) (522) (433) (542)
%e A370807 (2222) (3222) (442) (632)
%e A370807 (622) (722)
%e A370807 (3322) (3332)
%e A370807 (4222) (4322)
%e A370807 (22222) (5222)
%e A370807 (32222)
%t A370807 Table[Length[Select[IntegerPartitions[n],FreeQ[#,1] && Length[Select[Tuples[If[#==1,{},First/@FactorInteger[#]]&/@#],UnsameQ@@#&]]==0&]],{n,0,30}]
%Y A370807 These partitions are ranked by the odd terms of A355529, complement A368100.
%Y A370807 The version for set-systems is A367903, complement A367902.
%Y A370807 The version for factorizations is A368413, complement A368414.
%Y A370807 With ones allowed we have A370593, complement A370592.
%Y A370807 For a unique choice we have A370594, ranks A370647.
%Y A370807 The version for divisors instead of factors is A370804, complement A370805.
%Y A370807 A006530 gives greatest prime factor, least A020639.
%Y A370807 A027746 lists prime factors, A112798 indices, length A001222.
%Y A370807 A239312 counts condensed partitions, ranks A368110.
%Y A370807 A355741 counts choices of a prime factor of each prime index.
%Y A370807 Cf. A000040, A000720, A133686, A355739, A355740, A367771, A367867, A367905, A370583, A370585, A370586, A370636.
%K A370807 nonn,more
%O A370807 0,7
%A A370807 _Gus Wiseman_, Mar 04 2024