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A370807
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Number of integer partitions of n into parts > 1 such that it is not possible to choose a different prime factor of each part.
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5
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0, 0, 0, 0, 1, 0, 3, 1, 4, 4, 8, 9, 15, 17, 25, 30, 43, 54, 72, 87, 115, 139, 181, 224, 283, 342, 429, 519, 647, 779, 967
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OFFSET
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0,7
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LINKS
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EXAMPLE
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The a(0) = 0 through a(11) = 9 partitions:
. . . . (22) . (33) (322) (44) (333) (55) (443)
(42) (332) (432) (82) (533)
(222) (422) (522) (433) (542)
(2222) (3222) (442) (632)
(622) (722)
(3322) (3332)
(4222) (4322)
(22222) (5222)
(32222)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], FreeQ[#, 1] && Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]==0&]], {n, 0, 30}]
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CROSSREFS
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These partitions are ranked by the odd terms of A355529, complement A368100.
The version for divisors instead of factors is A370804, complement A370805.
A355741 counts choices of a prime factor of each prime index.
Cf. A000040, A000720, A133686, A355739, A355740, A367771, A367867, A367905, A370583, A370585, A370586, A370636.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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