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 A082020 Decimal expansion of 15/Pi^2. 21
 1, 5, 1, 9, 8, 1, 7, 7, 5, 4, 6, 3, 5, 0, 6, 6, 5, 7, 1, 6, 5, 8, 1, 9, 1, 9, 4, 8, 1, 4, 5, 9, 1, 4, 5, 8, 3, 5, 6, 5, 3, 8, 1, 6, 2, 0, 0, 8, 3, 6, 9, 8, 2, 3, 2, 6, 8, 4, 1, 3, 5, 4, 7, 8, 4, 1, 2, 5, 9, 6, 8, 1, 4, 4, 3, 3, 5, 3, 1, 6, 1, 7, 8, 6, 8, 1, 3, 9, 1, 0, 8, 8, 8, 4, 3, 2, 7, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 3/(2*Pi^2) (the same decimal expansion with an offset 0) is the probability that the greatest common divisor of two numbers selected at random is 2 (Christopher, 1956). - Amiram Eldar, May 23 2020 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 John Christopher, The Asymptotic Density of Some k-Dimensional Sets, The American Mathematical Monthly, Vol. 63, No. 6 (1956), pp. 399-401. Werner Hürlimann, Dedekind's arithmetic function and primitive four squares counting functions, Journal of Algebra, Number Theory: Advances and Applications, Vol. 14, No. 2 (2015), pp. 73-88. S. Ramanujan, Irregular numbers, J. Indian Math. Soc., Vol. 5 (1913), pp. 105-106. V. Sitaramaiah and M. V. Subbarao, Some asymptotic formulae involving powers of arithmetic functions, Number Theory, Madras 1987, Springer, 1989, pp. 201-234, alternative link (p. 230). Eric Weisstein's World of Mathematics, Prime Sums Eric Weisstein's World of Mathematics, Moebius Function Eric Weisstein's World of Mathematics, Prime Products FORMULA Product_{n >= 1} (1+1/prime(n)^2) = 15/Pi^2. - Ramanujan Equals Zeta(2)/Zeta(4) = A013661/A013662 = Sum_{n>=1} mu(n)^2/n^2 = Sum_{n>=1} |mu(n)|/n^2 . - Enrique Pérez Herrero, Jan 15 2012 Equals Sum_{n>=1} 1/A005117(n)^2 . - Enrique Pérez Herrero, Mar 30 2012 Equals lim_{n->oo} (1/n) * Sum_{k=1..n} psi(k)/k, where psi(k) is the Dedekind psi function (A001615) - Amiram Eldar, May 12 2019. EXAMPLE 1.51981775463506657... MAPLE evalf(15/Pi^2, 120); # G. C. Greubel, Oct 18 2019 MATHEMATICA A082020[digits_] := First[RealDigits[Zeta[2]/Zeta[4], 10, digits]]; A082020[100] (* Enrique Pérez Herrero, Jan 15 2012 *) RealDigits[15/Pi^2, 10, 120][[1]] (* Harvey P. Dale, Jun 23 2019 *) PROG (PARI) 15/Pi^2 \\ Michel Marcus, Oct 18 2019 (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); 15/Pi(R)^2; // G. C. Greubel, Oct 18 2019 (Sage) numerical_approx(15/pi^2, digits=100) # G. C. Greubel, Oct 18 2019 CROSSREFS Cf. A001615, A157290. Sequence in context: A154605 A114594 A021662 * A256559 A182498 A147406 Adjacent sequences:  A082017 A082018 A082019 * A082021 A082022 A082023 KEYWORD nonn,cons AUTHOR N. J. A. Sloane, May 09 2003 STATUS approved

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Last modified April 21 16:50 EDT 2021. Contains 343156 sequences. (Running on oeis4.)