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

Author

Juan Arias-de-Reyna, Sep 19 2015

Keywords

• nonn
• cons

Examples

			0.95592301586190237688406538670987007467715943165456868832805...
		

Links

• 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.

Crossrefs

Density of A209061.

Cf. A008683.

Programs

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 *)

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.