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A370320
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Number of non-condensed integer partitions of n, or partitions where it is not possible to choose a different divisor of each part.
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25
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0, 0, 1, 1, 2, 4, 6, 9, 13, 20, 28, 40, 54, 74, 102, 135, 180, 235, 310, 397, 516, 658, 843, 1066, 1349, 1687, 2119, 2634, 3273, 4045, 4995, 6128, 7517, 9171, 11181, 13579, 16457, 19884, 23992, 28859, 34646, 41506, 49634, 59211, 70533, 83836, 99504, 117867
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OFFSET
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0,5
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COMMENTS
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Includes all partitions containing 1.
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LINKS
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EXAMPLE
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The a(0) = 0 through a(8) = 13 partitions:
. . (11) (111) (211) (221) (222) (331) (611)
(1111) (311) (411) (511) (2222)
(2111) (2211) (2221) (3221)
(11111) (3111) (3211) (3311)
(21111) (4111) (4211)
(111111) (22111) (5111)
(31111) (22211)
(211111) (32111)
(1111111) (41111)
(221111)
(311111)
(2111111)
(11111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Length[Select[Tuples[Divisors/@#], UnsameQ@@#&]]==0&]], {n, 0, 30}]
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CROSSREFS
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The complement is counted by A239312 (condensed partitions).
These partitions have ranks A355740.
Factorizations in the case of prime factors are A368413, complement A368414.
The version for prime factors (not all divisors) is A370593, ranks A355529.
A355731 counts choices of a divisor of each prime index, firsts A355732.
Cf. A355535, A355739, A367867, A368097, A368110, A370583, A370584, A370594, A370806, A370807, A370808.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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