

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
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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

Table of n, a(n) for n=0..103.


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 (* JeanFrançois 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



