A325855 Number of strict integer partitions of n such that every pair of distinct parts has a different product.

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

Offset: 0

Author

Gus Wiseman, May 31 2019

Keywords

• nonn

Examples

			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)
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..250

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.

Programs

Mathematica

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