A218993 - OEIS

%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