A326849 - OEIS

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A326849

Number of integer partitions of n whose length times maximum is a multiple of n.

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

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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

Cf. A018818, A047993, A067538, A326837, A326842, A326843.

Sequence in context: A260895 A107753 A197929 * A328706 A342530 A240090

Adjacent sequences: A326846 A326847 A326848 * A326850 A326851 A326852

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 26 2019

STATUS

approved