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A137250
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Decimal expansion of the constant sum 1/(q*log(q)), summed over prime powers q>1.
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0
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2, 0, 0, 6, 6, 6, 6, 4, 5, 2, 8, 3, 1, 0, 6, 8, 7, 5, 6, 4, 3, 2, 2, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Evaluated from sum(m,k=1,2,3,..infinity) A008683(k)* I(k*m)/k^2, where I(x)=integral log zeta(t), t=x..infinity, is Cohen's underivative.
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REFERENCES
| D. A. Clark, An upper bound of sum 1/(a_i log a_i) for quasi-primitive sequences, Comp. Math. Appl., 35 (1998), 105-109. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 04 2008]
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LINKS
| H. Cohen, High precision computation of Hardy-Littlewood constants, preprint, 1998.
R. J. Mathar, Twenty digits of some Integrals of the Prime Zeta Function, arXiv:0811.4739 [math.NT]. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 04 2008, Jan 15 2009]
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FORMULA
| Equals sum 1/[ A000961(n)*log(A000961(n))], n=2,3,..., infinity.
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EXAMPLE
| 2.0066664528310687...
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CROSSREFS
| Sequence in context: A045866 A112964 A128613 * A161800 A100344 A094596
Adjacent sequences: A137247 A137248 A137249 * A137251 A137252 A137253
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KEYWORD
| more,nonn,cons
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AUTHOR
| R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 09 2008
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EXTENSIONS
| 8 more digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 04 2008
Changed preprint title R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 15 2009
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