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 A175640 Decimal expansion of Product_{p = prime} (1 +(3*p^2-1)/((p^2-1)*p*(p+1)) ). 1
 2, 5, 9, 6, 5, 3, 6, 2, 9, 0, 4, 5, 0, 5, 4, 2, 0, 7, 3, 6, 3, 2, 7, 4, 0, 6, 5, 6, 6, 6, 9, 5, 1, 6, 1, 4, 2, 3, 7, 3, 9, 4, 6, 3, 0, 5, 2, 3, 4, 5 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equals (29/18)*(61/48)*(397/360)*(1417/1344)*... inserting p=2, 3, 5, 7.. into the factor. LINKS M. B. Barban, The large sieve method and its application to number theory, Russ. Math. Surv. 21 (1) (1966) 49 MR 0199171. S. R. Finch, Class number theory [Cached copy, with permission of the author] Eric Weisstein's World of Mathematics, Barban's Constant Eric Weisstein's World of Mathematics, Prime Products Wikipedia, Euler Product EXAMPLE 2.596536290450542073632740... MAPLE read("transforms") : efact := 1+(3*p^2-1)/(p^2-1)/p/(p+1) ; Digits := 130 : tm := 380 : subs (p=1/x, 1/efact) ; taylor(%, x=0, tm) : L := [seq(coeftayl(%, x=0, i), i=1..tm-1)] : Le := EULERi(L) : x := 1.0 : for i from 2 to nops(Le) do x := x/evalf(Zeta(i))^op(i, Le) ; x := evalf(x) ; print(x) ; end do: MATHEMATICA digits = 50; \$MaxExtraPrecision = 5 digits; s = Log[(1 + (3*p^2 - 1)/((p^2 - 1)*p*(p + 1)))] + O[p, Infinity]^(12 digits) // Normal; B = Exp[s /. Power[p, k_] -> PrimeZetaP[-k]]; RealDigits[B, 10, digits][[1]] (* Jean-François Alcover, Jul 24 2017 *) CROSSREFS Sequence in context: A246206 A200336 A065225 * A204913 A198455 A018878 Adjacent sequences:  A175637 A175638 A175639 * A175641 A175642 A175643 KEYWORD cons,nonn AUTHOR R. J. Mathar, Aug 01 2010 EXTENSIONS More digits from Jean-François Alcover, Jul 24 2017 STATUS approved

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Last modified October 20 10:00 EDT 2019. Contains 328257 sequences. (Running on oeis4.)