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A175475 Decimal expansion of the Dickman function evaluated at 1/3. 5
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Density of the cube root-smooth numbers, see A090081. - Charles R Greathouse IV, Jul 14 2014
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.
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...
EXAMPLE
F(1/3) = 0.04860838829113156690718...
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 *)
PROG
(PARI) 1-log(3)+log(3)^2/2-Pi^2/12+polylog(2, 1/3) \\ Charles R Greathouse IV, Jul 14 2014
CROSSREFS
Sequence in context: A372355 A005133 A198241 * A193082 A348563 A201335
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, May 25 2010
STATUS
approved

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Last modified May 21 22:16 EDT 2024. Contains 372741 sequences. (Running on oeis4.)