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%I #7 Mar 13 2021 18:03:21
%S 1,1,2,3,5,7,11,15,22,30,42,56,76,100,133,171,225,287,369,467,592,740,
%T 931,1155,1435,1767,2178,2661,3254,3953,4798,5793,6991,8390,10069,
%U 12022,14346,17054,20255,23960,28334,33390,39308,46148,54116,63295,73967,86224
%N Number of integer partitions of n such that every pair of distinct parts has a different product.
%H Fausto A. C. Cariboni, <a href="/A325856/b325856.txt">Table of n, a(n) for n = 0..150</a>
%e The five partitions of 15 not satisfying the condition are:
%e (8,4,2,1)
%e (6,4,3,2)
%e (6,3,3,2,1)
%e (6,3,2,2,1,1)
%e (6,3,2,1,1,1,1)
%t Table[Length[Select[IntegerPartitions[n],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 Cf. A002033, A108917, A143823, A325853, A325854, A325857, A325858, A325877.
%K nonn
%O 0,3
%A _Gus Wiseman_, May 31 2019
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