This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A325854 #9 Feb 05 2022 02:31:35
%S A325854 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 A325854 132,151,173,206,226,263,297,337,387,427,488,555,623,697,782,886,984,
%U A325854 1108,1240,1374,1545,1726,1910,2120,2358,2614,2903,3218,3567,3933
%N A325854 Number of strict integer partitions of n such that every pair of distinct parts has a different quotient.
%C A325854 Also the number of strict integer partitions of n such that every pair of (not necessarily distinct) parts has a different product.
%H A325854 Fausto A. C. Cariboni, <a href="/A325854/b325854.txt">Table of n, a(n) for n = 0..300</a>
%e A325854 The a(1) = 1 through a(10) = 9 partitions (A = 10):
%e A325854 (1) (2) (3) (4) (5) (6) (7) (8) (9) (A)
%e A325854 (21) (31) (32) (42) (43) (53) (54) (64)
%e A325854 (41) (51) (52) (62) (63) (73)
%e A325854 (321) (61) (71) (72) (82)
%e A325854 (431) (81) (91)
%e A325854 (521) (432) (532)
%e A325854 (531) (541)
%e A325854 (621) (631)
%e A325854 (721)
%e A325854 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 A325854 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Divide@@@Subsets[Union[#],{2}]&]],{n,0,30}]
%Y A325854 The subset case is A325860.
%Y A325854 The maximal case is A325861.
%Y A325854 The integer partition case is A325853.
%Y A325854 The strict integer partition case is A325854.
%Y A325854 Heinz numbers of the counterexamples are given by A325994.
%Y A325854 Cf. A108917, A143823, A196724, A275972, A325768, A325855, A325858, A325868, A325869, A325876, A325877.
%K A325854 nonn
%O A325854 0,4
%A A325854 _Gus Wiseman_, May 31 2019