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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
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3, 3, 9, 0, 6, 4, 2, 0, 0, 5, 5, 7, 2, 5, 0, 3, 9, 1, 6, 1, 4, 2, 5, 9, 5, 6, 6, 3, 0, 0, 2, 6, 3, 0, 7, 9, 3, 7, 4, 0
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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
| Product_p sum_k=0^infinity 1/phi(p^k)^2 = product_p 1+p^2/((p-1)^2*(p^2-1)).
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EXAMPLE
| 3.3906420055...
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PROG
| (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
| Cf. A000010.
Sequence in context: A038068 A101126 A119006 * A010610 A140059 A070517
Adjacent sequences: A109692 A109693 A109694 * A109696 A109697 A109698
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KEYWORD
| cons,more,nonn
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Aug 07 2005
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EXTENSIONS
| Four more digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 03 2009, 25 more Dec 18 2010
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