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 A324754 Number of integer partitions of n containing no part > 1 whose prime indices all belong to the partition. 8
 1, 1, 2, 2, 4, 3, 7, 8, 11, 12, 19, 19, 30, 34, 46, 50, 71, 76, 104, 119, 151, 171, 225, 247, 315, 360, 446, 504, 629, 703, 867, 986, 1192, 1346, 1636, 1837, 2204, 2500, 2965, 3348, 3980, 4475, 5276, 5963, 6973, 7852, 9194, 10335, 12009, 13536, 15650, 17589 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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(1) = 1 through a(8) = 11  integer partitions:   (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)        (11)  (111)  (22)    (311)    (33)      (43)       (44)                     (31)    (11111)  (42)      (52)       (62)                     (1111)           (51)      (61)       (71)                                      (222)     (331)      (422)                                      (3111)    (511)      (611)                                      (111111)  (31111)    (2222)                                                (1111111)  (3311)                                                           (5111)                                                           (311111)                                                           (11111111) MATHEMATICA Table[Length[Select[IntegerPartitions[n], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]], {n, 0, 30}] CROSSREFS 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. Cf. A000837, A001462, A007097, A051424, A112798, A276625, A290822, A304360, A306844, A324695, A324750, A324755, A324760. Sequence in context: A240010 A283502 A324756 * A174220 A048675 A162474 Adjacent sequences:  A324751 A324752 A324753 * A324755 A324756 A324757 KEYWORD nonn AUTHOR Gus Wiseman, Mar 16 2019 STATUS approved

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Last modified March 29 18:37 EDT 2020. Contains 333117 sequences. (Running on oeis4.)