A376845 Decimal expansion of Product_{p prime} (p^5 + 1)/(p^5 - 1).

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

Offset: 1

Author

Stefano Spezia, Oct 06 2024

Keywords

• nonn
• cons

Examples

			1.0741508456720383646975062147556164766645757325...
		

References

• E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, second revised (Heath-Brown) edition, Oxford University Press, 1986. See equation 1.2.8 at p. 5.

Links

• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 111.

Crossrefs

Cf. A013663, A013668, A376742.

Programs

Mathematica

RealDigits[Zeta[5]^2/Zeta[10],10,100][[1]]

PARI

prodeulerrat((p^5 + 1)/(p^5 - 1))

Formula

Equals zeta(5)^2/zeta(10) = Sum_{k>=1} 2^omega(k)/k^5. See Titchmarsh and Shamos.