cp's OEIS Frontend

A068468 Decimal expansion of zeta(6)/(zeta(2)*zeta(3)).

%I A068468 #28 Nov 07 2022 07:39:38
%S A068468 5,1,4,5,1,0,1,0,1,5,0,8,3,9,3,1,2,3,0,7,3,2,8,1,1,8,6,7,7,2,7,8,9,6,
%T A068468 1,6,5,0,6,5,6,5,7,4,6,9,0,7,1,2,8,0,1,8,3,3,7,5,4,3,4,5,7,2,2,2,4,5,
%U A068468 5,1,4,9,4,9,3,8,2,4,9,4,6,7,7,3,2,3,8,4,2,4,7,8,6,8,7,5,9,7,4,8,0,8,4,6
%N A068468 Decimal expansion of zeta(6)/(zeta(2)*zeta(3)).
%H A068468 G. C. Greubel, <a href="/A068468/b068468.txt">Table of n, a(n) for n = 0..10000</a>
%H A068468 <a href="/index/Z#zeta_function">Index entries for zeta function</a>.
%F A068468 From _Amiram Eldar_, Nov 07 2022: (Start)
%F A068468 Equals 2*Pi^4/(315*zeta(3)).
%F A068468 Equals Product_{p prime} (1 - 1/(p^2-p+1)). (End)
%e A068468 0.514510101508393123073281186772789616506565746907128.....
%t A068468 RealDigits[Zeta[6]/(Zeta[2]*Zeta[3]), 10, 100][[1]] (* _G. C. Greubel_, Mar 11 2018 *)
%o A068468 (PARI) default(realprecision, 100); zeta(6)/(zeta(2)*zeta(3)) \\ _G. C. Greubel_, Mar 11 2018
%o A068468 (Magma) R:=RealField(150); SetDefaultRealField(R); L:=RiemannZeta(); 2*Pi(R)^4/(315*Evaluate(L,3)); // _G. C. Greubel_, Mar 11 2018
%Y A068468 Cf. A013661 (zeta(2)), A002117 (zeta(3)), A013664 (zeta(6)), A082695 (inverse).
%K A068468 cons,easy,nonn
%O A068468 0,1
%A A068468 _Benoit Cloitre_, Mar 10 2002