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A175639
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Decimal expansion of product_{p = prime} (1-3/p^3+2/p^4+1/p^5-1/p^6).
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2
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6, 7, 8, 2, 3, 4, 4, 9, 1, 9, 1, 7, 3, 9, 1, 9, 7, 8, 0, 3, 5, 5, 3, 8, 2, 7, 9, 4, 8, 2, 8, 9, 4, 8, 1, 4, 0, 9
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OFFSET
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0,1
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COMMENTS
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Equals (49/64)*(668/729)*(15304/15625)*(116724/117649)*... inserting p= A000040 = 2, 3, 5, 7.. into the factor. Slightly larger than product_{p=primes} (1-3/p^3) = 0.534566872085103888416775...
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LINKS
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Table of n, a(n) for n=0..37.
T. Taniguchi, A mean value theorem for the square of class number times regulator of quadratic extensions, arXiv:math/0410531
S. Finch, Class Number Theory
Eric Weisstein's World of Mathematics. Prime Products.
Eric Weisstein's World of Mathematics. Taniguchi's Constant.
Anonymous, Euler Product, Wikipedia
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EXAMPLE
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0.678234491917391978035...
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MAPLE
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read("transforms") : efact := 1-3/p^3+2/p^4+1/p^5-1/p^6 ; Digits := 130 : tm := 310 : 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: A113786 A004487 A010500 * A202346 A117022 A051994
Adjacent sequences: A175636 A175637 A175638 * A175640 A175641 A175642
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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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