A119964 Numerator of the n-th Artin product.

1, 5, 19, 779, 84911, 2632241, 713337311, 1163866139, 587752400195, 476667196558145, 2856927907113011, 345688276760674331, 13819099649042566549, 4988694973304366524189, 10780569837310736058772429

Offset: 1

Author

Alexander Adamchuk, Aug 03 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 product is Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}].

Links

• Eric Weisstein's World of Mathematics, Artin's Constant.

Crossrefs

Cf. A119534, A091568, A091567, A005596, A048296.

Programs

Mathematica

Table[Numerator[Product[1-1/(Prime[k]*(Prime[k]-1)),{k,1,n}]],{n,1,20}]

Formula

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