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A326851 Number of strict integer partitions of n whose length and maximum both divide n. 8
1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 2, 3, 1, 5, 1, 6, 1, 1, 1, 16, 1, 1, 1, 12, 1, 33, 1, 15, 1, 1, 1, 60, 1, 1, 1, 51, 1, 81, 1, 31, 57, 1, 1, 216, 1, 55, 1, 45, 1, 230, 1, 223, 1, 1, 1, 800, 1, 1, 314, 273, 1, 607, 1, 81, 1, 315, 1, 2404, 1, 1, 319 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Table of n, a(n) for n=0..75.

EXAMPLE

The a(6) = 2 through a(24) = 16 partitions (1 terms not shown):

  6       12        15          16        18      20           24

  3,2,1   6,4,2     5,4,3,2,1   8,4,3,1   9,5,4   10,5,3,2     12,7,5

          6,5,1                 8,5,2,1   9,6,3   10,5,4,1     12,8,4

          6,3,2,1                         9,7,2   10,6,3,1     12,9,3

                                          9,8,1   10,7,2,1     12,10,2

                                                  10,4,3,2,1   12,11,1

                                                               8,7,5,4

                                                               8,7,6,3

                                                               12,5,4,3

                                                               12,6,4,2

                                                               12,6,5,1

                                                               12,7,3,2

                                                               12,7,4,1

                                                               12,8,3,1

                                                               12,9,2,1

                                                               8,6,4,3,2,1

MATHEMATICA

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

CROSSREFS

The non-strict case is A326843.

Cf. A018818, A047993, A067538, A326837, A326842, A326849, A326852.

Sequence in context: A325403 A132068 A173441 * A129192 A062540 A173636

Adjacent sequences:  A326848 A326849 A326850 * A326852 A326853 A326854

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 26 2019

STATUS

approved

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Last modified May 31 07:09 EDT 2020. Contains 334747 sequences. (Running on oeis4.)