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A326842
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Number of integer partitions of n whose parts all divide n and whose length also divides n.
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18
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1, 1, 2, 2, 3, 2, 5, 2, 5, 3, 5, 2, 21, 2, 5, 6, 9, 2, 22, 2, 21, 6, 5, 2, 134, 3, 5, 6, 23, 2, 157, 2, 27, 6, 5, 6, 478, 2, 5, 6, 208, 2, 224, 2, 31, 63, 5, 2, 1720, 3, 30, 6, 34, 2, 322, 6, 295, 6, 5, 2, 13899, 2, 5, 68, 126, 8, 429, 2, 42, 6, 358, 2, 19959, 2
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OFFSET
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0,3
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COMMENTS
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The Heinz numbers of these partitions are given by A326847.
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LINKS
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EXAMPLE
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The a(1) = 1 through a(8) = 5 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (111) (22) (11111) (33) (1111111) (44)
(1111) (222) (2222)
(321) (4211)
(111111) (11111111)
The a(12) = 21 partitions:
(12)
(6,6)
(4,4,4)
(6,3,3)
(6,4,2)
(3,3,3,3)
(4,3,3,2)
(4,4,2,2)
(4,4,3,1)
(6,2,2,2)
(6,3,2,1)
(6,4,1,1)
(2,2,2,2,2,2)
(3,2,2,2,2,1)
(3,3,2,2,1,1)
(3,3,3,1,1,1)
(4,2,2,2,1,1)
(4,3,2,1,1,1)
(4,4,1,1,1,1)
(6,2,1,1,1,1)
(1,1,1,1,1,1,1,1,1,1,1,1)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n, All, Divisors[n]], Divisible[n, Length[#]]&]], {n, 1, 30}]
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CROSSREFS
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Partitions using divisors are A018818.
Partitions whose length divides their sum are A067538.
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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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