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

%I A325855 #9 Mar 12 2021 17:49:46
%S A325855 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,
%T A325855 129,152,173,198,232,260,302,342,386,448,498,565,646,728,819,918,1039,
%U A325855 1164,1310,1462,1631,1830,2053,2282,2532,2825,3136,3482,3869,4300,4744
%N A325855 Number of strict integer partitions of n such that every pair of distinct parts has a different product.
%H A325855 Fausto A. C. Cariboni, <a href="/A325855/b325855.txt">Table of n, a(n) for n = 0..250</a>
%e A325855 The a(1) = 1 through a(10) = 10 partitions (A = 10):
%e A325855   (1)  (2)  (3)   (4)   (5)   (6)    (7)    (8)    (9)    (A)
%e A325855             (21)  (31)  (32)  (42)   (43)   (53)   (54)   (64)
%e A325855                         (41)  (51)   (52)   (62)   (63)   (73)
%e A325855                               (321)  (61)   (71)   (72)   (82)
%e A325855                                      (421)  (431)  (81)   (91)
%e A325855                                             (521)  (432)  (532)
%e A325855                                                    (531)  (541)
%e A325855                                                    (621)  (631)
%e A325855                                                           (721)
%e A325855                                                           (4321)
%t A325855 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Times@@@Subsets[Union[#],{2}]&]],{n,0,30}]
%Y A325855 The subset case is A196724.
%Y A325855 The maximal case is A325859.
%Y A325855 The integer partition case is A325856.
%Y A325855 The strict integer partition case is A325855.
%Y A325855 Heinz numbers of the counterexamples are given by A325993.
%Y A325855 Cf. A002033, A108917, A143823, A275972, A325854, A325858, A325876, A325877.
%K A325855 nonn
%O A325855 0,4
%A A325855 _Gus Wiseman_, May 31 2019