A262276 Decimal expansion of Toth's constant (the density of the exponentially squarefree numbers).

9, 5, 5, 9, 2, 3, 0, 1, 5, 8, 6, 1, 9, 0, 2, 3, 7, 6, 8, 8, 4, 0, 6, 5, 3, 8, 6, 7, 0, 9, 8, 7, 0, 0, 7, 4, 6, 7, 7, 1, 5, 9, 4, 3, 1, 6, 5, 4, 5, 6, 8, 6, 8, 8, 3, 2, 8, 0, 5, 8, 9, 4, 9, 0, 1, 8, 1, 7, 2, 8, 7, 0, 1, 5, 5, 2, 2, 9, 2, 5, 7, 1, 0, 3, 5, 7, 2, 0, 0, 5, 5, 9, 1, 1, 6, 4, 4, 0, 3, 5, 2, 3, 0, 1, 2, 9, 3, 3, 4, 7, 1, 7, 1, 5, 8, 0, 1, 2, 2, 4, 3, 6, 3, 9, 8, 9, 3, 3, 8, 8, 1, 2, 0, 3, 8, 6, 6, 0, 1, 3, 2, 8, 6, 3, 2, 6, 7, 5, 2, 0, 6, 6, 3, 5, 8, 0, 2, 7, 1, 7, 9, 6, 0

Offset

0,1

Links

Table of n, a(n) for n=0..162.

Vladimir Shevelev, A fast computation of density of exponentially S-numbers, arXiv:1602.04244 [math.NT], 2016.

László Tóth, On certain arithmetic functions involving exponential divisors, II., Annales Univ. Sci. Budapest., Sect. Comp., 27 (2007), 155-166.

Formula

Equals Product_{prime p} (1+Sum_{j>=4} (mu(j)^2 - mu(j-1)^2)/p^j), where mu(n) is the Möbius function.

Example

0.95592301586190237688406538670987007467715943165456868832805...

Mathematica

$MaxExtraPrecision = m = 1000; f[x_] := Log[1 - x^4 + (1 - x)*Sum[x^e*(MoebiusMu[e]^2), {e, 4, m}]]; c = Rest[CoefficientList[Series[f[x], {x, 0, m}], x]*Range[0, m]]; RealDigits[Exp[NSum[Indexed[c, k]*PrimeZetaP[k]/k, {k, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 163][[1]] (* Amiram Eldar, Apr 27 2025 *)

Crossrefs

Density of A209061.

Cf. A008683.

Sequence in context: A155534 A154683 A200026 * A244844 A395729 A390072

Adjacent sequences: A262273 A262274 A262275 * A262277 A262278 A262279

Keyword

nonn,cons

Author

Juan Arias-de-Reyna, Sep 19 2015

Status

approved