This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A323669 #55 Feb 16 2025 08:33:57
%S A323669 7,5,9,9,0,8,8,7,7,3,1,7,5,3,3,2,8,5,8,2,9,0,9,5,9,7,4,0,7,2,9,5,7,2,
%T A323669 9,1,7,8,2,6,9,0,8,1,0,0,4,1,8,4,9,1,1,6,3,4,2,0,6,7,7,3,9,2,0,6,2,9,
%U A323669 8,4,0,7,2,1,6,7,6,5
%N A323669 Decimal expansion of 15/(2*Pi^2) = 1/((4/5)*zeta(2)).
%C A323669 This is the limit n -> infinity of (1/n^2)*Phi_1(n) = (1/n^2)*Sum_{k=1..n} psi(k), with Dedekind's psi function psi(k) = k*Product_{p|k} (1 + 1/p) = A001615(k). Distinct primes p dividing k appear, and the empty product for k = 1 is set to 1. See the Walfisz reference, Satz 2., p. 100 (with x -> n, and phi_1(n) = psi(n)).
%C A323669 For the rationals r(n) = (1/n^2)*Phi_1(n) see A327340(n)/A327341(n), n >= 1.
%D A323669 Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, p. 100, Satz 2.
%H A323669 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DedekindFunction.html">Dedekind Function</a>
%H A323669 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dedekind_psi_function"> Dedekind psi function</a>
%H A323669 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A323669 Equal to 15/(2*Pi^2) = 1/((4/5)*zeta(2)), with 1/zeta(2) = A059956.
%e A323669 0.7599088773175332858290959740729572917826908100418491163420677392062984...
%t A323669 RealDigits[15/2/Pi^2, 10, 100][[1]] (* _Amiram Eldar_, Sep 03 2019 *)
%o A323669 (PARI) 15/(2*Pi^2) \\ _Felix Fröhlich_, Sep 04 2019
%Y A323669 Cf. A001615, A059956 (1/zeta(2)), A327340, A327341.
%K A323669 nonn,cons,easy
%O A323669 0,1
%A A323669 _Wolfdieter Lang_, Sep 03 2019