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A325855 Number of strict integer partitions of n such that every pair of distinct parts has a different product. 10
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 14, 18, 22, 25, 31, 37, 44, 53, 59, 69, 83, 100, 111, 129, 152, 173, 198, 232, 260, 302, 342, 386, 448, 498, 565, 646, 728, 819, 918, 1039, 1164, 1310, 1462, 1631, 1830, 2053, 2282, 2532, 2825, 3136, 3482, 3869, 4300, 4744 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..55.

EXAMPLE

The a(1) = 1 through a(10) = 10 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)

                                     (421)  (431)  (81)   (91)

                                            (521)  (432)  (532)

                                                   (531)  (541)

                                                   (621)  (631)

                                                          (721)

                                                          (4321)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@Times@@@Subsets[Union[#], {2}]&]], {n, 0, 30}]

CROSSREFS

The subset case is A196724.

The maximal case is A325859.

The integer partition case is A325856.

The strict integer partition case is A325855.

Heinz numbers of the counterexamples are given by A325993.

Cf. A002033, A108917, A143823, A275972, A325854, A325858, A325876, A325877.

Sequence in context: A034141 A055002 A114097 * A174246 A083847 A034142

Adjacent sequences:  A325852 A325853 A325854 * A325856 A325857 A325858

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 31 2019

STATUS

approved

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Last modified August 26 01:32 EDT 2019. Contains 326324 sequences. (Running on oeis4.)