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A324754
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Number of integer partitions of n containing no part > 1 whose prime indices all belong to the partition.
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8
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..51.
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EXAMPLE
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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)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]], {n, 0, 30}]
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CROSSREFS
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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 A334871 A048675
Adjacent sequences: A324751 A324752 A324753 * A324755 A324756 A324757
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Mar 16 2019
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STATUS
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approved
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