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A370593
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Number of integer partitions of n such that it is not possible to choose a different prime factor of each part.
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33
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0, 1, 1, 2, 4, 5, 10, 12, 19, 26, 38, 51, 71, 94, 126, 165, 219, 285, 369, 472, 605, 766, 973, 1226, 1538, 1917, 2387, 2955, 3657, 4497, 5532, 6754, 8251, 10033, 12190, 14748, 17831, 21471, 25825, 30976, 37111, 44331, 52897, 62952, 74829, 88755, 105145, 124307
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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The a(0) = 0 through a(7) = 12 partitions:
. (1) (11) (21) (22) (41) (33) (61)
(111) (31) (221) (42) (322)
(211) (311) (51) (331)
(1111) (2111) (222) (421)
(11111) (321) (511)
(411) (2221)
(2211) (3211)
(3111) (4111)
(21111) (22111)
(111111) (31111)
(211111)
(1111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Length[Select[Tuples[If[#==1, {}, First/@FactorInteger[#]]&/@#], UnsameQ@@#&]]==0&]], {n, 0, 30}]
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CROSSREFS
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The complement for divisors instead of factors is A239312, ranks A368110.
For unlabeled multiset partitions we have A368097, complement A368098.
The complement is counted by A370592.
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
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AUTHOR
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STATUS
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approved
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