A175475 Decimal expansion of the Dickman function evaluated at 1/3.

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

Offset: 0

Author

R. J. Mathar, May 25 2010

Keywords

• cons
• nonn

Comments

Density of the cube root-smooth numbers, see A090081. - Charles R Greathouse IV, Jul 14 2014

Examples

			F(1/3) = 0.04860838829113156690718...
		

Links

• David Broadhurst, Dickman polylogarithms and their constants arXiv:1004.0519 [math-ph], 2010.
• K. Soundararajan, An asymptotic expansion related to the Dickman function, arXiv:1005.3494 [math.NT], 2010.

Crossrefs

Cf. A002391, A072691, A175478.

Programs

Mathematica

N[1 - Log[3] + Log[3]^2/2 - Pi^2/12 + PolyLog[2, 1/3], 105] // RealDigits // First // Prepend[#, 0]& (* Jean-François Alcover, Feb 05 2013 *)

PARI

1-log(3)+log(3)^2/2-Pi^2/12+polylog(2,1/3) \\ Charles R Greathouse IV, Jul 14 2014

Formula

Equals 1 - log(3) + log^2(3)/2 - Pi^2/12 + Sum_{n>=1} 1/(n^2*3^n), where Sum_{n>=1} 1/(n^2*3^n) = 0.3662132299770634876167462976642627638...