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Search: id:A124175
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| A124175 |
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Decimal expansion of Prod_{primes p} ((p-1)/p)^(1/p)). |
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+0
13
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| 5, 5, 9, 8, 6, 5, 6, 1, 6, 9, 3, 2, 3, 7, 3, 4, 8, 5, 7, 2, 3, 7, 6, 2, 2, 4, 4, 2, 2, 3, 4, 1, 6, 7, 1, 7, 2, 5, 7, 6, 6, 6, 3, 7, 0, 2, 1, 2, 9, 0, 6, 0, 3, 9, 5, 5, 4, 2, 3, 3, 9, 3, 3, 9, 3, 5, 2, 0, 3, 1, 7, 1, 7, 9, 7, 5, 9, 1, 5, 9, 3, 6, 2, 7, 6, 5, 4, 0, 9, 5, 0, 6, 3, 0, 6, 6, 5, 4, 7
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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This might be interpreted as the expected value of phi(n)/n for very large n.
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LINKS
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Eric Weisstein's World of Mathematics, Prime Zeta Function
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FORMULA
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exp(-suminf(h=1, primezeta(h+1)/h)) (Robert Gerbicz)
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EXAMPLE
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0.5598656169323734857237622442234167172576663702129060395542339339\
352031717975915936276540950630665470795373094197373037280781542375...
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PROGRAM
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(PARI) default(realprecision, 256); (f(k)=return(sum(n=1, 512, moebius(n)/n*log(zeta(k*n))))); exp(sum(h=1, 512, -1/h*f(h+1))) /*Robert Gerbicz*/
(PARI) exp(-suminf(m=2, log(zeta(m))*sumdiv(m, k, if(k<m, moebius(k)/(m-k), 0)))) /*Martin Fuller*/
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CROSSREFS
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Cf. A126226, A085548, A085541, A085964-A085969.
Sequence in context: A046600 A030798 A021951 this_sequence A168277 A163980 A011986
Adjacent sequences: A124172 A124173 A124174 this_sequence A124176 A124177 A124178
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KEYWORD
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nonn,cons
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AUTHOR
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David W. Wilson, Dec 05 2006
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EXTENSIONS
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Robert Gerbicz computed this to 130 decimal places.
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