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A324755
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Number of integer partitions of n not containing 1 or any part whose prime indices all belong to the partition.
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9
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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
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OFFSET
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0,5
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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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EXAMPLE
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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)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@If[k==1, {}, FactorInteger[k]]]]&]], {n, 0, 30}]
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CROSSREFS
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Cf. A000837, A001462, A051424, A112798, A276625, A290822, A304360, A306844, A324695, A324696, A324744.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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