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A175639 Decimal expansion of product_{p = prime} (1-3/p^3+2/p^4+1/p^5-1/p^6). 2
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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...

LINKS

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

EXAMPLE

0.678234491917391978035...

MAPLE

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:

CROSSREFS

Sequence in context: A113786 A004487 A010500 * A202346 A117022 A051994

Adjacent sequences:  A175636 A175637 A175638 * A175640 A175641 A175642

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Aug 01 2010

STATUS

approved

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Last modified October 23 17:37 EDT 2014. Contains 248468 sequences.