OFFSET
0,18
COMMENTS
Alternative name: Number of strict integer partitions of n that are either empty or (1) have smallest part not dividing all the others and (2) have greatest part divisible by all the others.
EXAMPLE
The a(11) = 1 through a(29) = 4 partitions (empty columns indicated by dots, A..O = 10..24):
632 . . . . . A52 . C43 . C432 C64 E72 . C643 . K52 . I92
C32 F53 C6432 K54
I32 O32
C632 I632
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], #=={}||UnsameQ@@#&&!And@@IntegerQ/@(#/Min@@#)&&And@@IntegerQ/@(Max@@#/#)&]], {n, 0, 30}]
CROSSREFS
The first condition alone gives A341450.
The second condition alone gives A343347.
The opposite (and dual) version is A343381.
A000009 counts strict partitions.
A000041 counts 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