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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

Table of n, a(n) for n=1..50.

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 December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)