cp's OEIS Frontend

A157295 Decimal expansion of 630/Pi^6.

%I A157295 #14 Jun 10 2023 03:09:22
%S A157295 6,5,5,3,0,1,7,2,8,1,7,6,3,8,6,9,4,6,5,3,6,5,9,7,7,0,9,9,9,5,9,4,9,4,
%T A157295 2,1,9,6,7,4,8,1,0,1,0,6,5,7,7,3,7,8,8,7,2,2,9,1,6,0,2,6,9,9,5,7,0,0,
%U A157295 1,6,9,4,2,2,9,7,9,1,6,1,6,5,3,9,3,2,6,3,6,9,8,5,2,1,9,6,9,4,7,7,0,2,7,6,5
%N A157295 Decimal expansion of 630/Pi^6.
%H A157295 Masato Kobayashi, <a href="https://arxiv.org/abs/2108.01822">Möbius functions of higher rank and Dirichlet series</a>, arXiv:2108.01822 [math.NT], 2021.
%H A157295 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A157295 Equals Product_{p primes = A000040} (1-1/p^2+1/p^4-1/p^6).
%F A157295 Equals A013662/(A013661*A013666).
%F A157295 Equals Product_{i>=1} (1-1/A001248(i)+1/A030514(i)-1/A030516(i)).
%F A157295 Equals 630*A092746.
%F A157295 Equals Sum_{n>=1} A363551(n)/n^2. - _Amiram Eldar_, Jun 10 2023
%e A157295 0.655301728176386946536... = (1-1/2^2+1/2^4-1/2^6)*(1-1/3^2+1/3^4-1/3^6)*(1-1/5^2+1/5^4-1/5^6)*(1-1/7^2+1/7^4-1/7^6)*...
%p A157295 evalf(630/Pi^6) ;
%t A157295 RealDigits[630/Pi^6, 10, 120][[1]] (* _Amiram Eldar_, Jun 10 2023 *)
%o A157295 (PARI) 630/Pi^6 \\ _Michel Marcus_, Aug 05 2021
%Y A157295 Cf. A013661, A013662, A013666, A001248, A030514, A030516, A092746, A363551.
%K A157295 cons,easy,nonn
%O A157295 0,1
%A A157295 _R. J. Mathar_, Feb 26 2009