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