OFFSET
0,3
COMMENTS
Also the number of integer partitions of n such that every orderless pair of (not necessarily distinct) parts has a different product.
EXAMPLE
The a(1) = 1 through a(7) = 14 partitions:
(1) (2) (3) (4) (5) (6) (7)
(11) (21) (22) (32) (33) (43)
(111) (31) (41) (42) (52)
(211) (221) (51) (61)
(1111) (311) (222) (322)
(2111) (321) (331)
(11111) (411) (511)
(2211) (2221)
(3111) (3211)
(21111) (4111)
(111111) (22111)
(31111)
(211111)
(1111111)
The one partition of 7 for which not every pair of distinct parts has a different quotient is (4,2,1).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@Divide@@@Subsets[Union[#], {2}]&]], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved