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A272300 Decimal expansion of lim_{N->infinity} (1/N^2 Sum_{n=1..N} K(n)), where K(n) is the squarefree kernel of n. 0
3, 5, 2, 2, 2, 1, 1, 0, 0, 4, 9, 9, 5, 8, 2, 7, 9, 6, 3, 6, 8, 3, 0, 1, 6, 7, 5, 1, 6, 3, 3, 1, 8, 6, 0, 5, 0, 9, 4, 2, 9, 3, 2, 1, 5, 7, 0, 8, 5, 4, 9, 0, 2, 4, 7, 0, 7, 1, 1, 3, 4, 2, 1, 2, 9, 5, 5, 4, 8, 5, 2, 8, 3, 4, 1, 0, 0, 3, 3, 8, 9, 2, 6, 8, 4, 0, 4, 1, 2, 2, 0, 7, 2, 8, 4, 6, 5, 6, 6, 8, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.5.1 Carefree couples, p. 111.

LINKS

Table of n, a(n) for n=0..100.

FORMULA

Equals (Pi^2/12)*A065464.

EXAMPLE

0.35222110049958279636830167516331860509429321570854902470711342...

MATHEMATICA

$MaxExtraPrecision = 800; digits = 101; terms = 2000; LR = Join[{0, 0}, LinearRecurrence[{-2, 0, 1}, {-2, 3, -6}, terms + 10]]; r[n_Integer] := LR[[n]]; (1/2)*Exp[NSum[r[n]*(PrimeZetaP[n - 1]/(n - 1)), {n, 3, terms}, NSumTerms -> terms, WorkingPrecision -> digits + 10, Method -> "AlternatingSigns"]] // RealDigits[#, 10, digits]& // First

CROSSREFS

Cf. A007947, A065464.

Sequence in context: A126353 A094791 A243524 * A115406 A059246 A091276

Adjacent sequences:  A272297 A272298 A272299 * A272301 A272302 A272303

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Apr 25 2016

STATUS

approved

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Last modified October 17 13:57 EDT 2019. Contains 328113 sequences. (Running on oeis4.)