A083344 a(n) = A082457(n) - A066715(n) = gcd(2n+1, A057643(2n+1)) - gcd(2n+1, A000203(2n+1)).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 30, 0, 0, 0, 0, 0, 0, 4, 0, 0

Offset: 1

Author

Labos Elemer, Apr 25 2003

Keywords

• sign

Examples

			n=22: 2n+1 = 45, A057643(45) = 5520, a(22) = gcd(45,5520) = 15 while A066715(45) = 3; a(22) = 15-3 = 12; sites where nonzero terms appear see in A082452.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768

Crossrefs

Cf. A057643, A066715, A000203, A082457, A082452.

Programs

Mathematica

di[x_] := Apply[LCM, Divisors[x]+1] (*A066715=*)t1=Table[GCD[2*n+1, DivisorSigma[1, 2*n+1]], {n, 1, 2048}]; (*A082457=*)t2=Table[GCD[2*w+1, di[1+2*w]], {w, 1, 2048}]; (*A083344=*)t2-t1;

PARI

a(n)=gcd(lcm(apply(d->d+1,divisors(2*n+1))),2*n+1)-gcd(sigma(2*n+1),2*n+1) \\ Charles R Greathouse IV, Feb 14 2013

Formula

a(n) = gcd(2n+1, lcm(1+D(2n+1))) - gcd(2n+1, sigma(2n+1)), gcd(2n+1, A057643(2n+1)) - gcd(2n+1, A000203(2n+1)), where D(x) is the set of divisors of x.