A120881 a(n) = number of k's, for 1 <= k <= n, where GCD(k,floor(n/k)) > 1.

0, 0, 0, 1, 1, 0, 0, 2, 3, 2, 2, 2, 2, 1, 1, 4, 4, 4, 4, 5, 4, 3, 3, 5, 6, 5, 7, 8, 8, 3, 3, 7, 7, 6, 6, 8, 8, 7, 6, 9, 9, 6, 6, 7, 9, 8, 8, 11, 12, 12, 12, 13, 13, 14, 13, 15, 14, 13, 13, 11, 11, 10, 11, 16, 16, 12, 12, 13, 13, 10, 10, 15, 15, 14, 15, 16, 16, 13, 13, 17

Offset

1,8

Comments

A120881(n) + A120882(n) = n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

For n = 8, we have the pairs {k,floor(n/k)} of {1,8},{2,4},{3,2},{4,2},{5,1},{6,1},{7,1},{8,1}. From these pairs we get the GCD's of 1,2,1,2,1,1,1,1. 2 of these GCD's are > 1. So a(8)= 2.

Mathematica

Table[Length[Select[Table[GCD[k, Floor[n/k]], {k, 1, n}], # > 1 &]], {n, 1, 80}] (* Stefan Steinerberger, Jul 23 2006 *)

Prog

(PARI) a(n) = sum(k=1, n, gcd(k, n\k) > 1); \\ Michel Marcus, Feb 16 2014

Crossrefs

Cf. A120882.

Sequence in context: A030329 A300139 A300666 * A297930 A031217 A064131

Adjacent sequences: A120878 A120879 A120880 * A120882 A120883 A120884

Keyword

nonn

Author

Leroy Quet, Jul 12 2006

Extensions

More terms from Stefan Steinerberger, Jul 23 2006

Status

approved