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

%I A079080 #17 Apr 07 2025 09:51:46
%S A079080 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,
%T A079080 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,
%U A079080 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
%N A079080 a(n) = gcd((prime(n)+1)*(prime(n+1)+1)/4, prime(n)*prime(n+1)+1).
%H A079080 Reinhard Zumkeller, <a href="/A079080/b079080.txt">Table of n, a(n) for n = 1..10000</a>
%F A079080 a(n) = gcd(A079079(n), A023523(n+1)).
%t A079080 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 *)
%o A079080 (Haskell)
%o A079080 a079080 n = a079079 n `gcd` a023523 (n + 1)
%o A079080 -- _Reinhard Zumkeller_, Oct 09 2012
%o A079080 (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
%Y A079080 Cf. A023523, A079079, A079081, A079082.
%K A079080 nonn
%O A079080 1,2
%A A079080 _Reinhard Zumkeller_, Dec 22 2002