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 A324754 #8 Mar 16 2019 10:13:04
%S A324754 1,1,2,2,4,3,7,8,11,12,19,19,30,34,46,50,71,76,104,119,151,171,225,
%T A324754 247,315,360,446,504,629,703,867,986,1192,1346,1636,1837,2204,2500,
%U A324754 2965,3348,3980,4475,5276,5963,6973,7852,9194,10335,12009,13536,15650,17589
%N A324754 Number of integer partitions of n containing no part > 1 whose prime indices all belong to the partition.
%C A324754 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C A324754 For example, (6,2) is such a partition because the prime indices of 6 are {1,2}, which do not all belong to the partition. On the other hand, (5,3) is not such a partition because the prime indices of 5 are {3}, and 3 belongs to the partition.
%e A324754 The a(1) = 1 through a(8) = 11 integer partitions:
%e A324754 (1) (2) (3) (4) (5) (6) (7) (8)
%e A324754 (11) (111) (22) (311) (33) (43) (44)
%e A324754 (31) (11111) (42) (52) (62)
%e A324754 (1111) (51) (61) (71)
%e A324754 (222) (331) (422)
%e A324754 (3111) (511) (611)
%e A324754 (111111) (31111) (2222)
%e A324754 (1111111) (3311)
%e A324754 (5111)
%e A324754 (311111)
%e A324754 (11111111)
%t A324754 Table[Length[Select[IntegerPartitions[n],!MemberQ[#,k_/;SubsetQ[#,PrimePi/@First/@FactorInteger[k]]]&]],{n,0,30}]
%Y A324754 The subset version is A324738, with maximal case A324744. The strict case is A324749. The Heinz number version is A324759. An infinite version is A324694.
%Y A324754 Cf. A000837, A001462, A007097, A051424, A112798, A276625, A290822, A304360, A306844, A324695, A324750, A324755, A324760.
%K A324754 nonn
%O A324754 0,3
%A A324754 _Gus Wiseman_, Mar 16 2019