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

Author

Gus Wiseman, Jul 26 2019

Keywords

• nonn

Comments

The Heinz numbers of these partitions are given by A326848.

Examples

			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.
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..160

Crossrefs

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

Programs

Mathematica

Table[If[n==0,1,Length[Select[IntegerPartitions[n],Divisible[Max[#]*Length[#],n]&]]],{n,0,30}]