A325854 Number of strict integer partitions of n such that every pair of distinct parts has a different quotient.

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.

Cf. A108917, A143823, A196724, A275972, A325768, A325855, A325858, A325868, A325869, A325876, A325877.

Sequence in context: A018125 A292420 A161654 * A301370 A342520 A225482

Adjacent sequences: A325851 A325852 A325853 * A325855 A325856 A325857

Keyword

nonn

Author

Gus Wiseman, May 31 2019

Status

approved