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 A324755 Number of integer partitions of n not containing 1 or any part whose prime indices all belong to the partition. 9
 1, 0, 1, 1, 2, 1, 4, 3, 5, 6, 10, 7, 16, 14, 23, 23, 35, 34, 53, 54, 75, 80, 112, 115, 160, 169, 223, 244, 315, 339, 442, 478, 604, 664, 832, 910, 1131, 1245, 1524, 1689, 2054, 2263, 2743, 3039, 3634, 4042, 4809, 5343, 6326, 7035, 8276, 9217, 10795, 12011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS 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. 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. LINKS EXAMPLE The a(2) = 1 through a(10) = 10 integer partitions (A = 10):   (2)  (3)  (4)   (5)  (6)    (7)   (8)     (9)    (A)             (22)       (33)   (43)  (44)    (54)   (55)                        (42)   (52)  (62)    (63)   (64)                        (222)        (422)   (72)   (73)                                     (2222)  (333)  (82)                                             (522)  (433)                                                    (442)                                                    (622)                                                    (4222)                                                    (22222) MATHEMATICA Table[Length[Select[IntegerPartitions[n], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@If[k==1, {}, FactorInteger[k]]]]&]], {n, 0, 30}] CROSSREFS The subset version is A324739, with maximal case A324762. The strict case is A324750. The Heinz number version is A324760. An infinite version is A324694. Cf. A000837, A001462, A051424, A112798, A276625, A290822, A304360, A306844, A324695, A324696, A324744. Sequence in context: A269595 A055176 A118267 * A259019 A262663 A075348 Adjacent sequences:  A324752 A324753 A324754 * A324756 A324757 A324758 KEYWORD nonn AUTHOR Gus Wiseman, Mar 16 2019 STATUS approved

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Last modified January 20 10:32 EST 2022. Contains 350472 sequences. (Running on oeis4.)