A120425 a(n) = maximum value among all k where 1<=k<=n of GCD(k,ceiling(n/k)).

1, 1, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 4, 4, 4, 4, 3, 3, 3, 3, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 5, 5, 7, 7, 7, 7, 7, 7, 7, 5, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 6, 6, 6, 6, 6, 6, 6, 6, 9, 9, 9, 9, 9, 9, 9, 9, 9, 5, 5, 5, 7, 7, 7, 7, 7, 7, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Offset

1,3

Links

Table of n, a(n) for n=1..100.

Example

For n = 10, we have the pairs {k,ceiling(n/k)} of {1,10},{2,5},{3,4},{4,3},{5,2},{6,2},{7,2},{8,2},{9,2},{10,1}. The GCD's of these 10 pairs are 1,1,1,1,1,2,1,2,1,1. Of these, 2 is the largest. So a(10) = 2.

Mathematica

Table[Max[Table[GCD[k, Ceiling[n/k]], {k, 1, n}]], {n, 1, 100}] (* Stefan Steinerberger, Jul 22 2006 *)

Crossrefs

Sequence in context: A328204 A194320 A231555 * A104186 A350399 A347648

Adjacent sequences: A120422 A120423 A120424 * A120426 A120427 A120428

Keyword

nonn

Author

Leroy Quet, Jul 12 2006

Extensions

More terms from Stefan Steinerberger, Jul 22 2006

Status

approved