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A324757
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Number of integer partitions of n not containing 1 or any prime indices of the parts.
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3
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1, 0, 1, 1, 2, 1, 4, 3, 4, 6, 9, 7, 14, 12, 19, 21, 28, 29, 41, 45, 56, 64, 81, 89, 114, 125, 154, 176, 211, 236, 288, 324, 383, 432, 514, 578, 678, 766, 891, 1006, 1176, 1306, 1525, 1711, 1966, 2212, 2538, 2839, 3258, 3646, 4150, 4647, 5288, 5891, 6698, 7472
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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.
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LINKS
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EXAMPLE
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The a(2) = 1 through a(10) = 9 integer partitions:
(2) (3) (4) (5) (6) (7) (8) (9) (A)
(22) (33) (43) (44) (54) (55)
(42) (52) (422) (63) (64)
(222) (2222) (72) (73)
(333) (82)
(522) (433)
(442)
(4222)
(22222)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&Intersection[#, PrimePi/@First/@Join@@FactorInteger/@#]=={}&]], {n, 0, 30}]
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CROSSREFS
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Cf. A000720, A000837, A001462, A051424, A112798, A276625, A290822, A304360, A306844, A324764, A324742, A324753, A324756.
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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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