A375887 Decimal expansion of Product_{n>=2} zeta(n)^n.

9, 7, 6, 6, 8, 2, 5, 8, 2, 1, 4, 5, 3, 2, 8, 9, 6, 9, 9, 2, 3, 0, 6, 8, 2, 6, 9, 5, 6, 4, 0, 7, 9, 2, 1, 6, 2, 0, 2, 8, 9, 8, 7, 9, 5, 0, 9, 6, 7, 2, 8, 0, 9, 2, 8, 4, 8, 8, 8, 3, 3, 0, 5, 1, 4, 0, 0, 2, 2, 7, 0, 8, 9, 8, 0, 3, 6, 0, 4, 4, 8, 7, 1, 3, 8, 6, 8, 0, 9, 7, 3, 8, 3, 4, 9, 2, 6, 2, 5, 6, 5, 5, 0, 2, 5, 7, 9, 3, 0, 8, 4, 9, 0, 2, 8, 7, 8, 3, 9, 6, 9, 3, 2, 2, 2, 9, 6, 4, 7, 3

Offset: 1

Author

Richard R. Forberg, Sep 01 2024

Keywords

• nonn
• cons

Comments

It is interesting to note that this product is very close in value to 3 * Sum_{n>=2} (zeta(n)^n-1), A375920, where that factor's first 30 digits are: 3.00012312615292744064909403341.

Examples

			9.766825821453289699230682695640792162028987950967280928488833051400227...
		

Crossrefs

Cf. A375920,(Sum_{n>=2} (zeta(n)^n-1)), A021002 (Product_{n>=2} zeta(n)), A093720 (Sum_{n >= 2} zeta(n)/n!), A013661 (zeta(2)).

Programs

Maple

evalf(Product(Zeta(n)^n, n = 2 .. infinity), 150); # Vaclav Kotesovec, Sep 02 2024

Mathematica

RealDigits[N[Product[Zeta[n]^n, {n, 2, 500}], 150]][[1]]

PARI

prodinf(k = 2, zeta(k)^k) \\ Amiram Eldar, Sep 02 2024