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

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