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%I #12 Sep 08 2022 08:45:25
%S 5,19,41,109,109,271,271,271,811,929,929,929,929,2161,2161,2161,3659,
%T 4421,4969,4969,4969,4969,4969,9311,10099,10099,10099,10099,10099,
%U 16001,17029,17029,19181,22051,22051,22051,22051,22051,22051,22051,32579
%N Largest prime divisor of numerator of the n-th Artin's product.
%C Artin's constant (A005596) is equal to Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,Infinity}]. n-th Artin's product is Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]. a(n) is prime from A091568 of the form p^2-p-1, where p is prime from A091567.
%H Amiram Eldar, <a href="/A119534/b119534.txt">Table of n, a(n) for n = 2..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ArtinsConstant.html">Artin's Constant</a>.
%F a(n) = Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]]]].
%t Table[Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]]]],{n,2,100}]
%o (Magma) [Max(PrimeDivisors(Numerator(&*[1-1/(NthPrime(k)^2-NthPrime(k)):k in [1..n]]))): n in [2..45]]; // _Marius A. Burtea_, Feb 18 2020
%Y Cf. A091568, A091567, A005596, A048296.
%K frac,nonn
%O 2,1
%A _Alexander Adamchuk_, Jul 27 2006
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