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.

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.

Links

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

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

Cf. A007947, A065463, A065464.

Sequence in context: A094791 A243524 A349988 * A115406 A059246 A091276

Adjacent sequences: A272297 A272298 A272299 * A272301 A272302 A272303

Keyword

nonn,cons

Author

Jean-François Alcover, Apr 25 2016

Status

approved