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%I #32 Aug 12 2022 19:21:02
%S 4,9,7,7,0,0,3,0,2,4,7,0,7,4,5,3,4,7,4,7,4,3,7,7,3,4,4,3,2,5,4,1,5,1,
%T 5,0,5,7,1,5,9,8,9,3,3,6,4,7,6,1,8,4,3,7,1,7,1,8,7,1,7,9,9,8,1,3,3,8,
%U 7,6,2,4,5,8,1,3,4,8,4,7,7,0,8,7,7,6,7,4,5,8,7,4,0,8,2,8,6,3,9,0,7,4,0,4,8,1
%N Decimal expansion of log(Pi^2/6).
%H Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/2424112/infinite-series-involving-von-mangoldts-function/2424151">Infinite series involving Von Mangoldt's function.</a>
%H Grant Sanderson, <a href="https://www.youtube.com/watch?v=4PDoT7jtxmw&t=1875s">What makes the natural log "natural"?</a>, 3Blue1Brown video (2020).
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MangoldtFunction.html">Mangold Function</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeZetaFunction.html">Prime Zeta Function</a>.
%F Equals Sum_{k>=2} MangoldtLambda(k) / ((k^2)*log(k)).
%F Equals Sum_{k>=1} (1/k)*(1/(A246655(n)^2)) where k is the exponent of the prime power, A025474(n+1).
%F Equals Sum_{k>=1} primezeta(2*k)/k.
%F Equals 2*log(Pi) - log(6).
%F Equals log(zeta(2)) = log(A013661).
%e Equals 1/(2^2) + 1/(3^2) + (1/(4^2))*(1/2) + 1/(5^2) + + 1/(7^2) + (1/(8^2))*(1/3) + ... = 0.4977003024707...
%t RealDigits[Log[Pi^2/6], 10, 120][[1]]
%t RealDigits[Sum[PrimeZetaP[2 k]/k, {k, 1, inf}], 10, 120][[1]]
%o (PARI) log(Pi^2/6) \\ _Michel Marcus_, Sep 15 2020
%Y Cf. A000796, A013661, A053510, A131659, A016629.
%Y Cf. A100995, A014963, A025474, A246655.
%K nonn,cons
%O 0,1
%A _Terry D. Grant_, Sep 11 2020
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