

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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 integer partition case is A325853.
The strict integer partition case is A325854.
Heinz numbers of the counterexamples are given by A325994.
Cf. A108917, A143823, A196724, A275972, A325768, A325855, A325858, A325868, A325869, A325876, A325877.


KEYWORD

nonn


AUTHOR



STATUS

approved



