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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 (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

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.

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:

CROSSREFS

Sequence in context: A118907 A200336 A065225 * A204913 A198455 A018878

Adjacent sequences:  A175637 A175638 A175639 * A175641 A175642 A175643

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Aug 01 2010

STATUS

approved

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Last modified August 2 02:25 EDT 2014. Contains 245138 sequences.