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 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.
A167865 counts strict chains of divisors > 1 summing to n.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 19 2021
STATUS
approved