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Silverman Constant

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The Silverman constant is defined by

sum_(n=1)^(infty)1/(phi(n)sigma_1(n))=product_(p prime)(1+sum_(k=1)^(infty)1/(p^(2k)-p^(k-1)))
(1)
=1.786576459365922463458590475541...
(2)

(OEIS A093827), where phi(n) is the totient function and sigma_1(n) is the divisor function.

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References

Finch, S. "Series Involving Arithmetric Functions." Jan. 24, 2007. https://web.archive.org/web/20160419152954/http://www.people.fas.harvard.edu/~sfinch/csolve/arth.pdf.Rusin, D. "Re: A Peculiar Sum." In The Mathematical Atlas. Mar. 27, 1996. https://web.archive.org/web/20140427083120/https://www.math.niu.edu/~rusin/known-math/96/numtheor.series.Sloane, N. J. A. Sequence A093827 in "The On-Line Encyclopedia of Integer Sequences."Zimmermann, P. "Re: A Peculiar Sum." Mar. 29, 1996. https://web.archive.org/web/20011123043051/http://www.mathsoft.com:80/asolve/constant/totient/zimmermn.html.

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Silverman Constant

Cite this as:

Weisstein, Eric W. "Silverman Constant." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SilvermanConstant.html

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