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%I #9 Feb 05 2022 02:31:35
%S 1,1,1,2,2,3,4,4,6,8,9,12,13,16,20,23,30,33,41,47,52,61,75,90,98,116,
%T 132,151,173,206,226,263,297,337,387,427,488,555,623,697,782,886,984,
%U 1108,1240,1374,1545,1726,1910,2120,2358,2614,2903,3218,3567,3933
%N Number of strict integer partitions of n such that every pair of distinct parts has a different quotient.
%C Also the number of strict integer partitions of n such that every pair of (not necessarily distinct) parts has a different product.
%H Fausto A. C. Cariboni, <a href="/A325854/b325854.txt">Table of n, a(n) for n = 0..300</a>
%e The a(1) = 1 through a(10) = 9 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 (431) (81) (91)
%e (521) (432) (532)
%e (531) (541)
%e (621) (631)
%e (721)
%e The two strict partitions of 13 such that not every pair of distinct parts has a different quotient are (9,3,1) and (6,4,2,1).
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Divide@@@Subsets[Union[#],{2}]&]],{n,0,30}]
%Y The subset case is A325860.
%Y The maximal case is A325861.
%Y The integer partition case is A325853.
%Y The strict integer partition case is A325854.
%Y Heinz numbers of the counterexamples are given by A325994.
%Y Cf. A108917, A143823, A196724, A275972, A325768, A325855, A325858, A325868, A325869, A325876, A325877.
%K nonn
%O 0,4
%A _Gus Wiseman_, May 31 2019
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