A116921 a(n) = largest integer <= n/2 which is coprime to n.

0, 1, 1, 1, 2, 1, 3, 3, 4, 3, 5, 5, 6, 5, 7, 7, 8, 7, 9, 9, 10, 9, 11, 11, 12, 11, 13, 13, 14, 13, 15, 15, 16, 15, 17, 17, 18, 17, 19, 19, 20, 19, 21, 21, 22, 21, 23, 23, 24, 23, 25, 25, 26, 25, 27, 27, 28, 27, 29, 29, 30, 29, 31, 31, 32, 31, 33, 33, 34, 33, 35, 35, 36, 35, 37, 37

Offset

1,5

Comments

a(n) + A116922(n) = n. For n>= 3, A116922(n) - a(n) is 1 if n is odd, is 2 if n is a multiple of 4 and is 4 if n is congruent to 2 (mod 4).

The arithmetic function v+-(n,2) as defined in A290988. - Robert Price, Aug 22 2017

Links

Table of n, a(n) for n=1..76.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

For n >= 3, a(n) = (n-1)/2 if n is odd, a(n) = n/2 - 1 if n is a multiple of 4 and a(n) = n/2 - 2 if n is congruent to 2 (mod 4).

a(n) = (2*n-4-2*(-1)^n+(-1)^(n/2)+(-1)^(3*n/2))/4, n>2. - Wesley Ivan Hurt, May 26 2015

For n > 2, a(n) = (n-2+cos(n*Pi/2)-cos(n*Pi))/2. - Wesley Ivan Hurt, Oct 02 2017

G.f.: t^2*(1+t^3-2*t^4+2*t^5)/((1-t)*(1-t^4)). - Mamuka Jibladze, Aug 22 2019

Mathematica

Join[{0, 1}, Table[(2 n - 4 - 2 (-1)^n + (-1)^(n/2) + (-1)^(3 n/2))/4, {n, 3, 50}]] (* Wesley Ivan Hurt, May 26 2015 *)
Table[Which[OddQ[n], (n-1)/2, Divisible[n, 4], n/2-1, Mod[n, 4]==2, n/2-2], {n, 80}]//Abs (* Harvey P. Dale, Jun 24 2017 *)

Prog

(Magma) [0] cat [(2*n-4-2*(-1)^n+(-1)^(n div 2)+(-1)^(3*n div 2)) div 4: n in [3..80]]; // Vincenzo Librandi, May 26 2015
(PARI) a(n) = {forstep(k = n\2, 0, -1, if (gcd(n, k) == 1, return (k)); ); } \\ Michel Marcus, May 26 2015
(PARI) a(n) = {if(n%2, (n-1)/2, if(n==2, 1, n/2 - if(n%4, 2, 1)))} \\ Andrew Howroyd, Aug 22 2019

Crossrefs

Cf. A116922, A290988.

Sequence in context: A328518 A163281 A307857 * A173989 A093068 A097357

Adjacent sequences: A116918 A116919 A116920 * A116922 A116923 A116924

Keyword

easy,nonn

Author

Leroy Quet, Feb 26 2006

Extensions

More terms from Wyatt Lloyd (wal118(AT)psu.edu), Mar 25 2006

Status

approved