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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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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)) }
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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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Adjacent sequences: A083278 A083279 A083280 this_sequence A083282 A083283 A083284
Sequence in context: A138500 A103985 A086279 this_sequence A019711 A010545 A019790
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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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