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A326852
Number of non-constant integer partitions of n whose length and maximum both divide n.
6
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 16, 0, 1, 7, 11, 0, 30, 0, 40, 18, 1, 0, 201, 0, 1, 38, 124, 0, 426, 0, 211, 73, 1, 48, 1391, 0, 1, 131, 1741, 0, 1774, 0, 951, 2145, 1, 0, 8345, 0, 1853, 381, 2382, 0, 6718, 2761, 10633, 623, 1, 0, 68037
OFFSET
0,13
COMMENTS
The Heinz numbers of these partitions are given by A326838.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..180
EXAMPLE
The a(6) = 1 through a(16) = 11 partitions (empty columns not shown):
(321) (4211) (52111) (633) (7211111) (53322) (8332)
(642) (53331) (8422)
(651) (54222) (8431)
(4332) (54321) (8521)
(4422) (54411) (8611)
(4431) (55221) (42222211)
(6222) (55311) (43222111)
(6321) (43321111)
(6411) (44221111)
(322221) (44311111)
(332211) (82111111)
(333111)
(422211)
(432111)
(441111)
(621111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !SameQ@@#&&Divisible[n, Length[#]]&&Divisible[n, Max[#]]&]], {n, 0, 30}]
CROSSREFS
The possibly constant case is A326843.
The strict case is A326851.
Sequence in context: A228574 A007791 A294699 * A070570 A347158 A347160
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved