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%I #15 Mar 24 2015 10:05:13
%S 2,3,2,5,3,7,2,3,2,11,4,13,2,5,2,17,3,19,5,7,2,23,4,5,2,3,7,29,6,31,2,
%T 3,2,7,4,37,2,3,5,41,7,43,2,5,2,47,4,7,2,3,2,53,3,11,8,3,2,59,6,61,2,
%U 9,2,13,3,67,2,3,7,71,9,73,2,5,2,11,3,79,5,3,2
%N Numerator of the least reduced fraction b/c > 1 using divisors b and c of n.
%C The product b*c divides n. Does every positive integer except one occur infinitely many times?
%H Clark Kimberling, <a href="/A218993/b218993.txt">Table of n, a(n) for n = 2..10000</a>
%e For n = 2,...,12, the fractions are 2/1, 3/1, 2/1, 5/1, 3/2, 7/1, 2/1, 3/1, 2/1, 11/1, 4/3, so that
%e A218993 = (2, 3, 2, 5, 3, 7, 2, 3, 2, 11, 4, ... );
%e A219093 = (1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, ... );
%e A219094 = (1, 1, 2, 1, 1, 1, 4, 3, 5, 1, 1, ... );
%e A219095 = (6, 12, 15, 18, 20, 21, 24, 28, 30, 35, 36, ... ).
%t f[n_] := Divisors[n];
%t t = Table[Min[Table[f[n][[i + 1]]/f[n][[i]], {i, 1, -1 + Length[f[n]]}]], {n, 2, 200}];
%t tn = Numerator[t] (* A218993 *)
%t td = Denominator[t] (* A219093 *)
%t Table[n/(tn[[n - 1]]*td[[n - 1]]),
%t {n,2,100}] (* A219094 *)
%t p[n_] := If[IntegerQ[t[[n]]], 0, 1]
%t u = Table[p[n], {n, 1, Length[t]}];1 + Flatten[Position[u, 1]] (* A219095 *)
%Y Cf. A219093, A219094, A219095.
%K nonn,easy
%O 2,1
%A _Clark Kimberling_, Feb 06 2013
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