A082452 -id:A082452 - cp's OEIS frontend

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

Labos Elemer, Apr 25 2003

sign

			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.

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

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

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;

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

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.

A082453 a(n)=2n+1 where n is such that A083344(n) is zero.

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137

Offset: 1

Labos Elemer, Apr 25 2003

nonn

			First two missing odd numbers are 45 and 75; missing terms are in A082452.

Cf. A057643, A066715, A000203, A082457, A083344.

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=*)t3=t2-t1; (*A082453=*)1+2*Flatten[Position[Abs[Sign[t3]], 0]];

cp's OEIS Frontend

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

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