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 A104141 Decimal expansion of 3/Pi^2. 14
 3, 0, 3, 9, 6, 3, 5, 5, 0, 9, 2, 7, 0, 1, 3, 3, 1, 4, 3, 3, 1, 6, 3, 8, 3, 8, 9, 6, 2, 9, 1, 8, 2, 9, 1, 6, 7, 1, 3, 0, 7, 6, 3, 2, 4, 0, 1, 6, 7, 3, 9, 6, 4, 6, 5, 3, 6, 8, 2, 7, 0, 9, 5, 6, 8, 2, 5, 1, 9, 3, 6, 2, 8, 8, 6, 7, 0, 6, 3, 2, 3, 5, 7, 3, 6, 2, 7, 8, 2, 1, 7, 7, 6, 8, 6, 5, 5, 1, 2, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 3/Pi^2 is the limit of (Sum_{k=1..n} phi(k))/n^2, where phi(k) is Euler's totient A000010(k), i.e., of A002088(n)/A000290(n) as n tends to infinity. The previous comment in the context of Farey series means that the length of the n-th Farey series can be approximated by multiplying this constant by n^2, "and that the approximation gets proportionally better as n gets larger", according to Conway and Guy. - Alonso del Arte, May 28 2011 The density of the anti-tau numbers, A046642 (see Zelinsky link theorem 57 page 15). - Michel Marcus, May 31 2015 The asymptotic density of the sequences of squarefree numbers with even number of prime factors (A030229), odd number of prime factors (A030059), and coprime to 6 (A276378). - Amiram Eldar, May 22 2020 REFERENCES J. H. Conway and R. K. Guy, The Book of Numbers, New York: Springer-Verlag, 1995, p. 156 L. E. Dickson, History of the Theory of Numbers, Vol. I pp. 126 Chelsea NY 1966. LINKS Joshua Zelinsky, Tau Numbers: A Partial Proof of a Conjecture and Other Results, Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.8. FORMULA Equals Sum_{n>=1} 1/A039956(n)^2. - Amiram Eldar, May 22 2020 From Terry D. Grant, Oct 31 2020: (Start) Equals (-1)*zeta(0)/zeta(2). Equals 1/(zeta(2)/2). Equals 1/A195055. Equals (1/2)*Sum_{k>=1} mu(k)/k^2. (End) EXAMPLE 3/Pi^2 = 0.303963550927013314331638389629... MATHEMATICA l = RealDigits[N[3/Pi^2, 100]]; Prepend[First[l], Last[l]] (* Ryan Propper, Aug 04 2005 *) PROG (PARI) 3/Pi^2 \\ Charles R Greathouse IV, Mar 08 2013 CROSSREFS Cf. A000010, A002088, A000290. Cf. A046642, A030229, A030059, A039956, A276378. Cf. A013661, A195055, A306633, A082020, A088246. Sequence in context: A132330 A117078 A021333 * A279977 A060533 A177785 Adjacent sequences:  A104138 A104139 A104140 * A104142 A104143 A104144 KEYWORD nonn,cons AUTHOR Lekraj Beedassy, Mar 07 2005 EXTENSIONS More terms from Ryan Propper, Aug 04 2005 STATUS approved

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Last modified April 16 23:40 EDT 2021. Contains 343051 sequences. (Running on oeis4.)