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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.

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:

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

STATUS

approved

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Last modified December 10 03:42 EST 2016. Contains 278993 sequences.