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 A068982 Decimal expansion of the limit of the product of a modified Zeta function. 3
 4, 3, 5, 7, 5, 7, 0, 7, 6, 7, 7, 2, 6, 4, 5, 5, 9, 3, 7, 3, 7, 6, 2, 2, 9, 7, 0, 1, 2, 0, 9, 4, 1, 8, 6, 3, 4, 9, 6, 8, 6, 4, 1, 7, 4, 9, 2, 4, 3, 6, 8, 0, 3, 8, 1, 7, 5, 4, 6, 0, 9, 8, 9, 0, 9, 2, 3, 0, 0, 2, 3, 6, 0, 1, 6, 1, 0, 3, 0, 5, 3, 1, 8, 8, 0, 4, 3, 9, 7, 9, 5, 9, 7, 7, 2, 3, 4, 0, 6, 5, 3, 7, 6, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The "modified Zeta function" Zetam(n) = sum(mu(k)/k^n) may be helpful when searching for a closed form for Apery's constant. LINKS FORMULA Product(Sum(mu(k)/k^n)), k=1..infinity, n=2..infinity Equals 1/A021002. - R. J. Mathar, Jan 31 2009 EXAMPLE 0.43575707... MAPLE with(numtheory); evalf(Product(Sum('mobius(k)/k^n', 'k'=1..infinity), n=2..infinity), 40); Note: For practical reasons you should change "infinity" to some finite value. evalf(product(1/Zeta(n), n=2..infinity), 120); # Vaclav Kotesovec, Oct 22 2014 MATHEMATICA digits = 104; 1/NProduct[ Zeta[n], {n, 2, Infinity}, WorkingPrecision -> digits+10, NProductFactors -> 1000] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 15 2013 *) CROSSREFS Cf. A021002, A002117. Sequence in context: A000211 A059902 A304225 * A317530 A171021 A035427 Adjacent sequences:  A068979 A068980 A068981 * A068983 A068984 A068985 KEYWORD cons,nonn AUTHOR Andre Neumann Kauffman (andrekff(AT)hotmail.com), Apr 01 2002 EXTENSIONS Corrected and extended by R. J. Mathar, Jan 31 2009 Example corrected by R. J. Mathar, Jul 23 2009 STATUS approved

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)