OFFSET
0,8
COMMENTS
Alternative name: Number of strict integer partitions of n that are empty or have greatest part not divisible by all the others.
EXAMPLE
The a(5) = 1 through a(12) = 9 partitions:
(3,2) (3,2,1) (4,3) (5,3) (5,4) (6,4) (6,5) (7,5)
(5,2) (4,3,1) (7,2) (7,3) (7,4) (5,4,3)
(5,2,1) (4,3,2) (5,3,2) (8,3) (6,4,2)
(5,3,1) (5,4,1) (9,2) (6,5,1)
(7,2,1) (5,4,2) (7,3,2)
(4,3,2,1) (6,4,1) (7,4,1)
(7,3,1) (8,3,1)
(5,3,2,1) (9,2,1)
(5,4,2,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], #=={}||UnsameQ@@#&&!And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
CROSSREFS
The dual strict complement is A097986.
The dual version is A341450.
The strict complement is counted by A343347.
The case with smallest part not divisible by all the others is A343379.
The case with smallest part divisible by all the others is A343381.
A000005 counts divisors.
A000009 counts strict partitions.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
A167865 counts strict chains of divisors > 1 summing to n.
A339564 counts factorizations with a selected factor.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 16 2021
STATUS
approved