login
A339660
Number of strict integer partitions of n with no 1's and a part divisible by all the other parts.
3
1, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 1, 3, 3, 3, 3, 5, 2, 5, 5, 4, 5, 7, 3, 5, 6, 5, 5, 9, 4, 7, 6, 6, 9, 11, 6, 9, 10, 9, 10, 12, 6, 11, 12, 10, 12, 16, 9, 15, 16, 12, 14, 18, 14, 16, 18, 14, 15, 22, 11, 16, 20, 13, 21, 23, 15, 21, 24, 21, 21, 31, 14, 24
OFFSET
0,7
COMMENTS
Alternative name: Number of strict integer partitions of n with no 1's that are empty or have greatest part divisible by all the other parts.
EXAMPLE
The a(n) partitions for n = 14, 12, 18, 24, 30, 39, 36:
(14) (12) (18) (24) (30) (39) (36)
(12,2) (8,4) (12,6) (16,8) (24,6) (36,3) (27,9)
(8,4,2) (9,3) (15,3) (18,6) (25,5) (26,13) (30,6)
(10,2) (16,2) (20,4) (27,3) (27,9,3) (32,4)
(12,4,2) (21,3) (28,2) (28,7,4) (33,3)
(22,2) (20,10) (30,6,3) (34,2)
(12,6,4,2) (18,9,3) (24,12,3) (24,12)
(24,4,2) (24,8,4,3) (24,8,4)
(16,8,4,2) (20,10,5,4) (18,9,6,3)
(24,6,4,3,2) (24,6,4,2)
(20,10,4,2)
MATHEMATICA
Table[If[n==0, 1, Length[Select[IntegerPartitions[n], FreeQ[#, 1]&&UnsameQ@@#&&And@@IntegerQ/@(Max@@#/#)&]]], {n, 0, 30}]
CROSSREFS
The dual version is A098965 (non-strict: A083711).
The non-strict version is A339619 (Heinz numbers: complement of A343337).
The version with 1's allowed is A343347 (non-strict: A130689).
The case without a part dividing all the other parts is A343380.
A000009 counts strict partitions.
A000070 counts partitions with a selected part.
A015723 counts strict partitions with a selected part.
A018818 counts partitions into divisors (strict: A033630).
A167865 counts strict chains of divisors > 1 summing to n.
Sequence in context: A030371 A029550 A091110 * A104659 A077197 A320510
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 19 2021
STATUS
approved