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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
OFFSET
0,1
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.5.1 Carefree couples, p. 111.
FORMULA
Equals (Pi^2/12)*A065464.
Equals (1/2) * A065463. - Amiram Eldar, Nov 16 2021
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
PROG
(PARI) prodeulerrat(1 - 1/(p*(p+1)))/2 \\ Amiram Eldar, Nov 16 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved