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A285572 Number of finite sets of pairwise indivisible positive integers with least common multiple n.

%I A285572 #12 Sep 02 2017 03:04:36
%S A285572 1,1,1,1,1,2,1,1,1,2,1,3,1,2,2,1,1,3,1,3,2,2,1,4,1,2,1,3,1,9,1,1,2,2,
%T A285572 2,6,1,2,2,4,1,9,1,3,3,2,1,5,1,3,2,3,1,4,2,4,2,2,1,23,1,2,3,1,2,9,1,3,
%U A285572 2,9,1,10,1,2,3,3,2,9,1,5,1,2,1,23,2,2,2,4,1,23,2,3,2,2,2,6,1,3,3,6
%N A285572 Number of finite sets of pairwise indivisible positive integers with least common multiple n.
%H A285572 Michael De Vlieger, <a href="/A285572/b285572.txt">Table of n, a(n) for n = 1..10000</a>
%e A285572 The a(72)=10 sets are {72}, {8,9}, {8,18}, {8,36}, {9,24}, {18,24}, {24,36}, {6,8,9}, {8,9,12}, {8,12,18}.
%t A285572 nn=50;
%t A285572 stableSets[u_,Q_]:=If[Length[u]===0,{{}},With[{w=First[u]},Join[stableSets[DeleteCases[u,w],Q],Prepend[#,w]&/@stableSets[DeleteCases[u,r_/;r===w||Q[r,w]||Q[w,r]],Q]]]];
%t A285572 Table[Length[Select[Rest[stableSets[Divisors[n],Divisible]],LCM@@#===n&]],{n,1,nn}]
%Y A285572 Cf. A000666, A006126, A048143, A054921, A076078, A076413, A285573.
%K A285572 nonn
%O A285572 1,6
%A A285572 _Gus Wiseman_, Apr 21 2017