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A362296 Greatest common divisor of composite numbers between the n-th and (n+1)st primes.

%I A362296 #24 Apr 16 2023 15:55:24
%S A362296 4,6,1,12,1,18,1,1,30,1,1,42,1,1,1,60,1,1,72,1,1,1,1,1,102,1,108,1,1,
%T A362296 1,1,138,1,150,1,1,1,1,1,180,1,192,1,198,1,1,1,228,1,1,240,1,1,1,1,
%U A362296 270,1,1,282,1,1,1,312,1,1,1,1,348,1,1,1,1,1,1,1,1,1
%N A362296 Greatest common divisor of composite numbers between the n-th and (n+1)st primes.
%H A362296 Winston de Greef, <a href="/A362296/b362296.txt">Table of n, a(n) for n = 2..10000</a>
%F A362296 For n > 1, a(n)=prime(n)+1 if and only if prime(n+1)=prime(n)+2 and a(n)=1 otherwise.
%o A362296 (Python)
%o A362296 from sympy import prime, isprime
%o A362296 def A362296(n): return m-1 if isprime(m:=prime(n)+2) else 1
%o A362296 (PARI) a(n) = gcd([prime(n)+1..prime(n+1)-1]); \\ _Michel Marcus_, Apr 16 2023
%Y A362296 Cf. A056831 (LCM), A061214 (product).
%K A362296 nonn
%O A362296 2,1
%A A362296 _Chai Wah Wu_, Apr 15 2023