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Search: id:A109695
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| A109695 |
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Decimal expansion of sum_n=1^inf 1/phi(n)^2. |
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+0
1
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| 3, 3, 9, 0, 6, 4, 2, 0, 0, 5, 5, 7, 2, 5, 0
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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The logarithm of the value can be expanded in a series sum_{j=2..infinity} c(j)*P(j)=P(2)+2*P(3)+(7/2)*P(4)+... where P(.) is the prime zeta function. The partial sums of the series are a slowly oscillating function of the upper limit of j, from which the bracketing interval [3.390642005572503655...,3.390642005572504756..] for the constant can be computed. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 03 2009]
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FORMULA
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product_p sum_k=0^inf 1/phi(p^k)^2 product_p 1+p^2/((p-1)^2*(p^2-1))
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EXAMPLE
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3.3906420055...
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PROGRAM
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(PARI) N=1000000000 prodeuler(p=2, N, 1.+p^2/((p-1)^2*(p^2-1)))*(1+1/(N*log(N)))
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CROSSREFS
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Cf. phi A000010.
Sequence in context: A038068 A101126 A119006 this_sequence A010610 A140059 A070517
Adjacent sequences: A109692 A109693 A109694 this_sequence A109696 A109697 A109698
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KEYWORD
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cons,more,nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 07 2005
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EXTENSIONS
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Four more digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 03 2009
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