A325853 - OEIS

A325853

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

1, 1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 51, 69, 88, 116, 148, 193, 242, 309, 385, 484, 596, 746, 915, 1128, 1371, 1679, 2030, 2460, 2964, 3570, 4268, 5115, 6088, 7251, 8584, 10175, 12002, 14159, 16619, 19526, 22846, 26713, 31153, 36300, 42169, 48990, 56728

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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.

LINKS

Table of n, a(n) for n=0..47.

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

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. A002033, A103300, A108917, A143823, A196724, A325768, A325856, A325868, A325869, A325876.

Sequence in context: A035968 A112581 A288255 * A035976 A035985 A035995

Adjacent sequences: A325850 A325851 A325852 * A325854 A325855 A325856

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 31 2019

STATUS

approved