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A175640
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Decimal expansion of product_{p = prime} (1 +(3*p^2-1)/((p^2-1)*p*(p+1)) ).
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1
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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
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OFFSET
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1,1
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COMMENTS
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Equals (29/18)*(61/48)*(397/360)*(1417/1344)*... inserting p=2, 3, 5, 7.. into the factor.
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LINKS
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Table of n, a(n) for n=1..36.
S. Finch, Class Number Theory.
M. B. Barban, The large sieve method and its application to number theory, Russ. Math. Surv. 21 (1) (1966) 49 MR 0199171.
Eric Weisstein's World of Mathematics. Barban's Constant.
Eric Weisstein's World of Mathematics. Prime Products.
Anonymous, Euler Product, Wikipedia.
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EXAMPLE
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2.596536290450542073632740...
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MAPLE
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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:
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CROSSREFS
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Sequence in context: A118907 A200336 A065225 * A204913 A198455 A018878
Adjacent sequences: A175637 A175638 A175639 * A175641 A175642 A175643
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KEYWORD
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cons,nonn
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AUTHOR
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R. J. Mathar, Aug 01 2010
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STATUS
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approved
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