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A161166 Decimal expansion of a constant in the linear term in the growth rate of unitary squarefree divisors. 6
7, 4, 8, 3, 7, 2, 3, 3, 3, 4, 2, 9, 6, 7, 4, 7, 0, 0, 9, 3, 8, 0, 8, 6, 5, 2, 9, 4, 3, 9, 4, 0, 8, 9, 9, 5, 9, 9, 2, 9, 2, 5, 4, 0, 2, 5, 9, 4, 5, 6, 8, 9, 6, 6, 0, 0, 0, 8, 5, 5, 1, 3, 0, 8, 8, 5, 7, 5, 2, 5, 6, 7, 6, 9, 7, 5, 1, 3, 0, 8, 3, 9, 6, 4, 5, 9, 3, 8, 4, 2, 6, 2, 1, 1, 9, 7, 1, 0, 0, 8, 1, 5, 5, 6, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Other constituents of the linear term are in A065463, A073002, A001620 and A059956.

REFERENCES

D. Suryanarayana and V. Siva Rama Prasad, The number of k-ary, k+1-free divisors of an integer, J. Reine Angew. Math. 276 (1975) 15-35.

LINKS

Table of n, a(n) for n=0..105.

Steven R. Finch, Unitarism and Infinitarism, February 25, 2004. [Cached copy, with permission of the author]

FORMULA

Equals sum_{primes p} (2p+1)*log(p)/((p+1)(p^2+p-1)) = sum_p log(p)*[2/(p^2-1)-3/p^3-1)+4/(p^4-1)-10/(p^5-1)....] where the terms accumulate; this is essentially the logarithmic derivative of the Riemann zeta function at s=2, 3, 4,...

EXAMPLE

0.748372333429674...

MATHEMATICA

ratfun = (2*p + 1)/((p + 1)*(p^2 + p - 1)); zetas = 0; ratab = Table[konfun = Simplify[ratfun + c/(p^power - 1)] // Together; coefs = CoefficientList[Numerator[konfun], p]; sol = Solve[Last[coefs] == 0, c][[1]]; zetas = zetas + c*Zeta'[power]/Zeta[power] /. sol; ratfun = konfun /. sol, {power, 2, 25}]; Do[Print[N[Sum[Log[p]*ratfun /. p -> Prime[k], {k, 1, m}] + zetas, 120]], {m, 2000, 20000, 2000}] (* Vaclav Kotesovec, Jun 24 2020 *)

CROSSREFS

Sequence in context: A021576 A222183 A010509 * A199060 A330596 A296427

Adjacent sequences:  A161163 A161164 A161165 * A161167 A161168 A161169

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Jun 04 2009

EXTENSIONS

More digits from Vaclav Kotesovec, Jun 24 2020

STATUS

approved

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Last modified March 1 08:23 EST 2021. Contains 341732 sequences. (Running on oeis4.)