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 A335089 Decimal expansion of log(Pi^2/6). 0
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Math Stack Exchange, Infinite series involving Von Mangoldt's function. Grant Sanderson, What makes the natural log "natural"?, 3Blue1Brown video (2020). Eric Weisstein's World of Mathematics, Mangold Function. Eric Weisstein's World of Mathematics, Prime Zeta Function. FORMULA Equals Sum_{k>=2} MangoldtLambda(k) / ((k^2)*log(k)). Equals Sum_{k>=1} (1/k)*(1/(A246655(n)^2)) where k is the exponent of the prime power, A025474(n+1). Equals Sum_{k>=1} primezeta(2*k)/k. Equals 2*log(Pi) - log(6). Equals log(zeta(2)) = log(A013661). EXAMPLE 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... MATHEMATICA RealDigits[Log[Pi^2/6], 10, 120][[1]] RealDigits[Sum[PrimeZetaP[2 k]/k, {k, 1, inf}], 10, 120][[1]] PROG (PARI) log(Pi^2/6) \\ Michel Marcus, Sep 15 2020 CROSSREFS Cf. A000796, A013661, A053510, A131659, A016629. Cf. A100995, A014963, A025474, A246655. Sequence in context: A166923 A021205 A296425 * A306004 A056992 A339023 Adjacent sequences:  A335086 A335087 A335088 * A335090 A335091 A335092 KEYWORD nonn,cons AUTHOR Terry D. Grant, Sep 11 2020 STATUS approved

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Last modified August 5 04:03 EDT 2021. Contains 346457 sequences. (Running on oeis4.)