A079080 a(n) = gcd((prime(n)+1)*(prime(n+1)+1)/4, prime(n)*prime(n+1)+1).

1, 2, 12, 6, 6, 3, 18, 6, 4, 60, 4, 3, 42, 6, 4, 2, 30, 2, 6, 36, 8, 6, 2, 3, 3, 204, 6, 54, 3, 48, 6, 2, 138, 6, 300, 4, 2, 6, 4, 2, 90, 12, 96, 3, 396, 10, 14, 6, 114, 3, 8, 120, 6, 2, 4, 4, 540, 4, 3, 282, 6, 6, 6, 156, 3, 6, 2, 6, 174, 3, 4, 6, 4, 2, 6, 4, 3, 3, 15, 6, 210, 12, 216, 4, 6, 2

Offset: 1

Author

Reinhard Zumkeller, Dec 22 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023523, A079079, A079081, A079082.

Programs

Haskell

a079080 n = a079079 n `gcd` a023523 (n + 1)
-- Reinhard Zumkeller, Oct 09 2012

Mathematica

a[n_] := Module[{p = Prime[n], q}, q = NextPrime[p]; GCD[(p+1) * (q+1) / 4, p*q + 1]]; Array[a, 100] (* Amiram Eldar, Apr 06 2025 *)

PARI

a(n) = my(p = prime(n), q = nextprime(p+1)); gcd((p+1)*(q+1)/4, p*q+1); \\ Amiram Eldar, Apr 06 2025

Formula

a(n) = gcd(A079079(n), A023523(n+1)).