login
A326851
Number of strict integer partitions of n whose length and maximum both divide n.
13
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
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.
Sequence in context: A325403 A132068 A173441 * A129192 A062540 A173636
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved