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A326849 Number of integer partitions of n whose length times maximum is a multiple of n. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The Heinz numbers of these partitions are given by A326848.

LINKS

Table of n, a(n) for n=0..58.

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 A240090 A078224

Adjacent sequences:  A326846 A326847 A326848 * A326850 A326851 A326852

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 26 2019

STATUS

approved

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Last modified June 6 16:22 EDT 2020. Contains 334828 sequences. (Running on oeis4.)