login
A325854
Number of strict integer partitions of n such that every pair of distinct parts has a different quotient.
11
1, 1, 1, 2, 2, 3, 4, 4, 6, 8, 9, 12, 13, 16, 20, 23, 30, 33, 41, 47, 52, 61, 75, 90, 98, 116, 132, 151, 173, 206, 226, 263, 297, 337, 387, 427, 488, 555, 623, 697, 782, 886, 984, 1108, 1240, 1374, 1545, 1726, 1910, 2120, 2358, 2614, 2903, 3218, 3567, 3933
OFFSET
0,4
COMMENTS
Also the number of strict integer partitions of n such that every pair of (not necessarily distinct) parts has a different product.
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 0..300
EXAMPLE
The a(1) = 1 through a(10) = 9 partitions (A = 10):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
(21) (31) (32) (42) (43) (53) (54) (64)
(41) (51) (52) (62) (63) (73)
(321) (61) (71) (72) (82)
(431) (81) (91)
(521) (432) (532)
(531) (541)
(621) (631)
(721)
The two strict partitions of 13 such that not every pair of distinct parts has a different quotient are (9,3,1) and (6,4,2,1).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@Divide@@@Subsets[Union[#], {2}]&]], {n, 0, 30}]
CROSSREFS
The subset case is A325860.
The maximal case is A325861.
The integer partition case is A325853.
The strict integer partition case is A325854.
Heinz numbers of the counterexamples are given by A325994.
Sequence in context: A018125 A292420 A161654 * A301370 A342520 A225482
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 31 2019
STATUS
approved