A376742 Decimal expansion of Product_{p prime} (p^3 + 1)/(p^3 - 1).

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

Offset: 1

Author

Stefano Spezia, Oct 03 2024

Keywords

• nonn
• cons

Examples

			1.420308303489193353248184427065490...
		

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 pp. 408-409.

Crossrefs

Cf. A000578, A001221, A002117, A013664, A034444, A092732, A183030.

Programs

Mathematica

RealDigits[Zeta[3]^2/Zeta[6],10,100][[1]]

PARI

prodeulerrat((p^3 + 1)/(p^3 - 1))

Formula

Equals zeta(3)^2/zeta(6) = Sum_{k>=1} 2^omega(k)/k^3. See Titchmarsh and Shamos.

Equals 945*zeta(3)^2/Pi^6.

Equals A157289 / A088453 = A013664 / A347328^2. - R. J. Mathar, Jul 14 2025