A120886 a(n) = number of k's with 1 <= k <= n where gcd(k,ceiling(n/k)) > 1.

0, 0, 1, 1, 1, 1, 4, 4, 3, 2, 4, 4, 5, 5, 7, 8, 6, 6, 8, 8, 9, 9, 11, 11, 11, 10, 12, 10, 10, 10, 15, 15, 12, 13, 15, 15, 14, 14, 16, 16, 15, 15, 22, 22, 22, 22, 24, 24, 22, 21, 22, 23, 23, 23, 24, 24, 22, 22, 24, 24, 27, 27, 29, 27, 23, 23, 28, 28, 28, 29, 34, 34, 31, 31, 33, 32, 32

Offset

1,7

Comments

a(n) + A120887(n) = n.

Links

Table of n, a(n) for n=1..77.

Example

a(7)=4 because for k=1,2,...,7 we have gcd(k,ceiling(7/k))=1,2,3,2,1,2,1, respectively.

Maple

a:=proc(n) local ct, k: ct:=0: for k from 1 to n do if gcd(k, ceil(n/k))>1 then ct:=ct+1 else ct:=ct fi od: end: seq(a(n), n=1..87); # Emeric Deutsch, Jul 23 2006

Mathematica

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

Crossrefs

Cf. A120887.

Sequence in context: A194668 A138160 A364128 * A228777 A329205 A023402

Adjacent sequences: A120883 A120884 A120885 * A120887 A120888 A120889

Keyword

nonn

Author

Leroy Quet, Jul 12 2006

Extensions

More terms from Emeric Deutsch and Stefan Steinerberger, Jul 23 2006

Status

approved