A120887 - OEIS

A120887

a(n) is the number of k's in 1..n such that gcd(k,ceiling(n/k)) = 1.

1, 2, 2, 3, 4, 5, 3, 4, 6, 8, 7, 8, 8, 9, 8, 8, 11, 12, 11, 12, 12, 13, 12, 13, 14, 16, 15, 18, 19, 20, 16, 17, 21, 21, 20, 21, 23, 24, 23, 24, 26, 27, 21, 22, 23, 24, 23, 24, 27, 29, 29, 29, 30, 31, 31, 32, 35, 36, 35, 36, 34, 35, 34, 37, 42, 43, 39, 40, 41, 41, 37, 38, 42, 43, 42

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OFFSET

1,2

COMMENTS

A120886(n) + A120887(n) = n.

LINKS

Table of n, a(n) for n=1..75.

EXAMPLE

a(7)=3 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..85); # 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. A120882, A120886.

Sequence in context: A072813 A285106 A369429 * A155860 A318285 A318560

Adjacent sequences: A120884 A120885 A120886 * A120888 A120889 A120890

KEYWORD

nonn

AUTHOR

Leroy Quet, Jul 12 2006

EXTENSIONS

More terms from Emeric Deutsch and Stefan Steinerberger Jul 23 2006

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 12 2007

STATUS

approved