A326850 Number of strict integer partitions of n whose maximum part divides n.

0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 4, 1, 5, 2, 6, 1, 10, 1, 10, 5, 12, 1, 23, 1, 18, 15, 23, 1, 49, 1, 34, 36, 38, 1, 106, 1, 54, 79, 81, 1, 189, 1, 124, 162, 104, 1, 412, 1, 145, 307, 289, 1, 608, 12, 437, 559, 256, 1, 1432, 1, 340, 981, 976, 79, 1730, 1

Offset

0,7

Links

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300

Example

The initial terms count the following partitions:
   1: (1)
   2: (2)
   3: (3)
   4: (4)
   5: (5)
   6: (6)
   6: (3,2,1)
   7: (7)
   8: (8)
   8: (4,3,1)
   9: (9)
  10: (10)
  10: (5,4,1)
  10: (5,3,2)
  11: (11)
  12: (12)
  12: (6,5,1)
  12: (6,4,2)
  12: (6,3,2,1)
  13: (13)
  14: (14)
  14: (7,6,1)
  14: (7,5,2)
  14: (7,4,3)
  14: (7,4,2,1)
  15: (15)
  15: (5,4,3,2,1)

Mathematica

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Divisible[n, Max[#]]&]], {n, 0, 30}]

Crossrefs

Positions of 1's appear to be A308168.

The non-strict case is given by A067538.

Cf. A018818, A033630, A067538, A102627, A200745, A316413, A326625, A326836, A326843, A326851.

Sequence in context: A260438 A112197 A112198 * A303756 A105259 A224708

Adjacent sequences: A326847 A326848 A326849 * A326851 A326852 A326853

Keyword

nonn

Author

Gus Wiseman, Jul 28 2019

Status

approved