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A326849
Number of integer partitions of n whose length times maximum is a multiple of n.
16
1, 1, 2, 2, 3, 2, 6, 2, 5, 5, 10, 2, 19, 2, 18, 26, 24, 2, 55, 2, 87, 82, 60, 2, 207, 86, 106, 192, 363, 2, 668, 2, 527, 616, 304, 928, 1827, 2, 498, 1518, 3229, 2, 4294, 2, 4445, 6307, 1266, 2, 11560, 3629, 8280, 7802, 13633, 2, 19120, 18938, 31385, 16618, 4584
OFFSET
0,3
COMMENTS
The Heinz numbers of these partitions are given by A326848.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..160
EXAMPLE
The a(1) = 1 through a(9) = 5 partitions:
1 2 3 4 5 6 7 8 9
11 111 22 11111 33 1111111 44 333
1111 222 2222 621
411 4211 321111
3111 11111111 111111111
111111
For example, (4,1,1) is such a partition because its length times maximum is 3 * 4 = 12, which is a multiple of 6.
MATHEMATICA
Table[If[n==0, 1, Length[Select[IntegerPartitions[n], Divisible[Max[#]*Length[#], n]&]]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved