

A175640


Decimal expansion of product_{p = prime} (1 +(3*p^21)/((p^21)*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
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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^21)/(p^21)/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..tm1)] : 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



