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A119534 Largest prime divisor of numerator of the n-th Artin's product. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
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
Eric Weisstein's World of Mathematics, Artin's Constant.
FORMULA
a(n) = Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]]]].
MATHEMATICA
Table[Max[FactorInteger[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)), {k, 1, n}]]]], {n, 2, 100}]
PROG
(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
CROSSREFS
Sequence in context: A024841 A155737 A100572 * A306190 A033622 A091568
KEYWORD
frac,nonn
AUTHOR
Alexander Adamchuk, Jul 27 2006
STATUS
approved

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Last modified April 18 20:26 EDT 2024. Contains 371781 sequences. (Running on oeis4.)