A326851 - OEIS

A326851

Number of strict integer partitions of n whose length and maximum both divide n.

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

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OFFSET

0,7

LINKS

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..383

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