A218993 Numerator of the least reduced fraction b/c > 1 using divisors b and c of n.

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, 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, 9, 2, 13, 3, 67, 2, 3, 7, 71, 9, 73, 2, 5, 2, 11, 3, 79, 5, 3, 2

Offset

2,1

Comments

The product b*c divides n. Does every positive integer except one occur infinitely many times?

Links

Clark Kimberling, Table of n, a(n) for n = 2..10000

Example

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
A218993 = (2, 3, 2, 5, 3, 7, 2, 3, 2, 11, 4, ... );
A219093 = (1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, ... );
A219094 = (1, 1, 2, 1, 1, 1, 4, 3, 5, 1, 1, ... );
A219095 = (6, 12, 15, 18, 20, 21, 24, 28, 30, 35, 36, ... ).

Mathematica

f[n_] := Divisors[n];
t = Table[Min[Table[f[n][[i + 1]]/f[n][[i]], {i, 1, -1 + Length[f[n]]}]], {n, 2, 200}];
tn = Numerator[t]  (* A218993 *)
td = Denominator[t] (* A219093 *)
Table[n/(tn[[n - 1]]*td[[n - 1]]),
   {n, 2, 100}]  (* A219094 *)
p[n_] := If[IntegerQ[t[[n]]], 0, 1]
u = Table[p[n], {n, 1, Length[t]}]; 1 + Flatten[Position[u, 1]]  (* A219095 *)

Crossrefs

Cf. A219093, A219094, A219095.

Sequence in context: A210437 A109674 A284260 * A067629 A079870 A364156

Adjacent sequences: A218990 A218991 A218992 * A218994 A218995 A218996

Keyword

nonn,easy

Author

Clark Kimberling, Feb 06 2013

Status

approved