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A370804
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Number of non-condensed integer partitions of n into parts > 1.
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9
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0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 3, 6, 6, 12, 14, 21, 25, 37, 43, 62, 75, 101, 124, 167, 198, 261, 316, 401, 488, 618
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OFFSET
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0,10
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COMMENTS
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These are partitions without ones such that it is not possible to choose a different divisor of each part.
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LINKS
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EXAMPLE
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The a(6) = 1 through a(14) = 12 partitions:
(222) . (2222) (333) (3322) (3332) (3333) (4333) (4442)
(3222) (4222) (5222) (4422) (7222) (5333)
(22222) (32222) (6222) (33322) (5522)
(33222) (43222) (8222)
(42222) (52222) (33332)
(222222) (322222) (43322)
(44222)
(53222)
(62222)
(332222)
(422222)
(2222222)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], FreeQ[#, 1] && Length[Select[Tuples[Divisors/@#], UnsameQ@@#&]]==0&]], {n, 0, 30}]
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CROSSREFS
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These partitions have as ranks the odd terms of A355740.
The complement without ones is A370805.
A355731 counts choices of a divisor of each prime index, firsts A355732.
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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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