login
Number of positive integers, k, where k <= 2n+1 and gcd(k, 2n+1) = gcd(k+1, 2n+1) = 1.
3

%I #23 Aug 20 2024 11:27:24

%S 1,1,3,5,3,9,11,3,15,17,5,21,15,9,27,29,9,15,35,11,39,41,9,45,35,15,

%T 51,27,17,57,59,15,33,65,21,69,71,15,45,77,27,81,45,27,87,55,29,51,95,

%U 27,99,101,15,105,107,35,111,63,33,75,99,39,75,125,41,129,85,27,135,137

%N Number of positive integers, k, where k <= 2n+1 and gcd(k, 2n+1) = gcd(k+1, 2n+1) = 1.

%H Walter Klotz and Torsten Sander, <a href="https://doi.org/10.37236/963">Some Properties of Unitary Cayley Graphs</a>, The Electronic Journal of Combinatorics, Volume 14 (2007), #R45. See Corollary 7 p. 4.

%F a(n) = A058026(2*n+1). - _Ridouane Oudra_, Aug 20 2024

%p A070554:=proc(n) local p, a:=2*n+1; for p in numtheory[factorset](2*n+1) do a:=a*(1-2/p) end do; a end proc: seq(A070554(n), n=0..100); # _Ridouane Oudra_, Aug 20 2024

%o (PARI) a(n) = my(n = 2*n+1); n*prod(p=1, n, if (isprime(p) && !(n % p), (1-2/p), 1)); \\ _Michel Marcus_, Feb 02 2016

%Y Bisection of A058026.

%K nonn

%O 0,3

%A _Leroy Quet_, Nov 15 2000

%E More terms from _Sascha Kurz_, Feb 02 2003