A376742 - OEIS

%I #13 Oct 06 2024 14:35:27

%S 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,

%T 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,

%U 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

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

%D 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.

%H Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See pp. 408-409.

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

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

%e 1.420308303489193353248184427065490...

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

%o (PARI) prodeulerrat((p^3 + 1)/(p^3 - 1))

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

%K nonn,cons

%O 1,2

%A _Stefano Spezia_, Oct 03 2024