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Search: id:A083281
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| A083281 |
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Decimal expansion of h=prod(sqrt(p(p-1))*log(1/(1-1/p))) where p runs through the primes. |
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+0
1
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| 9, 6, 9, 2, 7, 6, 9, 4, 3, 8, 2, 7, 4, 9, 1, 6, 3, 0
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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Arises in formulae like: sum(k<=x,1/tau(kd))=hx/sqrt(Pi*log(x))*{ g(d)+O((3/4)^omega(d)/log(x)) } where g satisfies sum(d<=x,g(d))=x/h/sqrt(Pi*log(x))*{ 1+O(1/log(x)) }
The logarithm of the value has an expansion -P(2)/24 -P(3)/24 -109*P(4)/2880 -49*P(5)/1440-... in terms of the prime zeta functions P(.). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009]
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REFERENCES
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G. Tenenbaum, Introduction a la theorie analytique et probabiliste des nombres, collection SMF no. 1, 1995, p. 210
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FORMULA
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h= 0.96927694...
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PROGRAM
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(PARI) prod(k=1, 40000, sqrt(prime(k)*(prime(k)-1))*log(1/(1-1/prime(k))))
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CROSSREFS
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Sequence in context: A153071 A086279 A155533 this_sequence A019711 A010545 A019790
Adjacent sequences: A083278 A083279 A083280 this_sequence A083282 A083283 A083284
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KEYWORD
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cons,more,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 02 2003
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EXTENSIONS
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10 more digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 31 2009
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