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A334479
Decimal expansion of Product_{k>=1} (1 + 1/A007528(k)^3).
7
1, 0, 0, 9, 1, 3, 4, 5, 0, 8, 6, 3, 8, 4, 7, 4, 4, 7, 8, 0, 7, 1, 1, 3, 7, 5, 3, 9, 5, 8, 9, 2, 0, 5, 5, 8, 8, 1, 7, 4, 5, 6, 4, 7, 8, 5, 2, 9, 5, 2, 5, 5, 9, 9, 3, 0, 7, 2, 3, 6, 2, 0, 8, 1, 4, 8, 7, 9, 6, 2, 8, 3, 5, 9, 1, 6, 3, 6, 0, 3, 2, 1, 1, 9, 3, 2, 6, 6, 4, 3, 5, 2, 6, 4, 0, 4, 9, 6, 5, 9, 7, 5, 6, 1, 6
OFFSET
1,4
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 * zeta(s) / ((2^s + 1) * (3^s + 1) * zeta(2*s)).
FORMULA
A334479 / A334480 = 91*sqrt(3)*zeta(3)/(6*Pi^3).
A334477 * A334479 = 810*zeta(3)/Pi^6.
EXAMPLE
1.0091345086384744780711375395892055881745647852...
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, May 02 2020
EXTENSIONS
More digits from Vaclav Kotesovec, Jun 27 2020
STATUS
approved