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A326843
Number of integer partitions of n whose length and maximum both divide n.
21
1, 1, 2, 2, 3, 2, 5, 2, 5, 3, 5, 2, 22, 2, 5, 11, 16, 2, 36, 2, 46, 22, 5, 2, 209, 3, 5, 42, 130, 2, 434, 2, 217, 77, 5, 52, 1400, 2, 5, 135, 1749, 2, 1782, 2, 957, 2151, 5, 2, 8355, 3, 1859, 385, 2388, 2, 6726, 2765, 10641, 627, 5, 2, 68049, 2, 5, 13424, 17142
OFFSET
0,3
COMMENTS
The Heinz numbers of these partitions are given by A326837.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..180
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) = 22 partitions:
(12)
(6,6)
(4,4,4)
(6,3,3)
(6,4,2)
(6,5,1)
(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[If[n==0, 1, Length[Select[IntegerPartitions[n], Divisible[n, Length[#]]&&Divisible[n, Max[#]]&]]], {n, 0, 30}]
CROSSREFS
The strict case is A326851.
The non-constant case is A326852.
The case where all parts (not just the maximum) divide n is A326842.
Sequence in context: A342086 A272209 A326842 * A323347 A322900 A238791
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved