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A334480 Decimal expansion of Product_{k>=1} (1 - 1/A007528(k)^3). 5
9, 9, 0, 8, 8, 4, 1, 4, 5, 5, 2, 5, 2, 1, 3, 3, 5, 6, 5, 6, 3, 4, 0, 3, 1, 7, 3, 5, 5, 9, 4, 3, 2, 7, 5, 1, 6, 4, 3, 4, 8, 3, 1, 2, 1, 7, 5, 0, 0, 7, 6, 1, 3, 3, 0, 4, 8, 6, 7, 7, 4, 7, 8, 4, 9, 4, 3, 1, 7, 8, 8, 8, 2, 5, 7, 6, 7, 4, 3, 1, 7, 7, 5, 2, 7, 6, 3, 4, 5, 2, 1, 7, 8, 9, 8, 8, 9, 2, 9, 2, 1, 3, 5, 4, 6, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

In general, for s > 0, Product_{k>=1} (1 + 1/A007528(k)^(2*s+1)) / (1 - 1/A007528(k)^(2*s+1)) = (1 - 1/2^(2*s + 1)) * (3^(2*s + 1) - 1) * (2*s)! * zeta(2*s + 1) / (sqrt(3) * A002114(s) * Pi^(2*s + 1)).

For s > 1, Product_{k>=1} (1 + 1/A007528(k)^s) / (1 - 1/A007528(k)^s) = (2^s - 1) * (3^s - 1) * zeta(s) / (zeta(s, 1/6) - zeta(s, 5/6)).

For s > 1, Product_{k>=1} (1 - 1/A002476(k)^s) * (1 - 1/A007528(k)^s) = 6^s / ((2^s - 1)*(3^s - 1)*zeta(s)).

LINKS

Table of n, a(n) for n=0..105.

R. J. Mathar, Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli, arXiv:1008.2547 [math.NT], p. 26 (case 6 5 3 = 1/A334480).

FORMULA

A334479 / A334480 = 91*sqrt(3)*zeta(3)/(6*Pi^3).

A334478 * A334480 = 108/(91*zeta(3)).

EXAMPLE

0.990884145525213356563403173559432751643483121750...

CROSSREFS

Cf. A007528, A175646, A334425, A334427, A334479.

Sequence in context: A257176 A324859 A090655 * A229758 A076115 A014726

Adjacent sequences:  A334477 A334478 A334479 * A334481 A334482 A334483

KEYWORD

nonn,cons,changed

AUTHOR

Vaclav Kotesovec, May 02 2020

EXTENSIONS

More digits from Vaclav Kotesovec, Jun 27 2020

STATUS

approved

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)