A119534 Largest prime divisor of numerator of the n-th Artin's product.

5, 19, 41, 109, 109, 271, 271, 271, 811, 929, 929, 929, 929, 2161, 2161, 2161, 3659, 4421, 4969, 4969, 4969, 4969, 4969, 9311, 10099, 10099, 10099, 10099, 10099, 16001, 17029, 17029, 19181, 22051, 22051, 22051, 22051, 22051, 22051, 22051, 32579

Offset: 2

Author

Alexander Adamchuk, Jul 27 2006

Keywords

• frac
• nonn

Comments

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 2..1000
• Eric Weisstein's World of Mathematics, Artin's Constant.

Crossrefs

Cf. A091568, A091567, A005596, A048296.

Programs

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

Mathematica

Table[Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]]]],{n,2,100}]

Formula

a(n) = Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]]]].