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A326842
Number of integer partitions of n whose parts all divide n and whose length also divides n.
18
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
OFFSET
0,3
COMMENTS
The Heinz numbers of these partitions are given by A326847.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..419
EXAMPLE
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)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n, All, Divisors[n]], Divisible[n, Length[#]]&]], {n, 1, 30}]
CROSSREFS
Partitions using divisors are A018818.
Partitions whose length divides their sum are A067538.
Sequence in context: A180125 A342086 A272209 * A326843 A323347 A322900
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved