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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
OFFSET
0,1
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Terry D. Grant, Sep 11 2020
STATUS
approved