|
|
A246749
|
|
Decimal expansion of F'(rho), an auxiliary constant associated with the asymptotic number of values of the Euler totient function less than a given number, where the function F and the constant rho are defined in A246746.
|
|
1
|
|
|
5, 6, 9, 7, 7, 5, 8, 9, 3, 4, 2, 3, 0, 1, 9, 2, 6, 7, 5, 7, 5, 2, 9, 1, 3, 7, 0, 4, 6, 8, 5, 2, 4, 7, 8, 9, 7, 8, 5, 8, 1, 0, 1, 9, 8, 2, 1, 7, 8, 3, 5, 7, 3, 5, 9, 3, 4, 5, 9, 5, 6, 7, 1, 7, 5, 8, 4, 1, 1, 4, 4, 0, 5, 3, 8, 6, 6, 0, 6, 7, 7, 6, 8, 3, 1, 7, 8, 4, 7, 5, 1, 5, 7, 4, 3, 8, 9, 2, 8, 8, 5
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
Let F(x) = sum_{k >= 1} ((k+1)*log(k+1) - k*log(k) - 1)*x^k.
F'(rho), where rho is the unique solution on [0,1) of F(rho)=1,
|
|
EXAMPLE
|
5.6977589342301926757529137046852478978581019821783573593459567...
|
|
MATHEMATICA
|
digits = 101; F[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*x^k, {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; F'[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*k*x^(k - 1), {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; rho = x /. FindRoot[F[x] == 1, {x, 5/10, 6/10}, WorkingPrecision -> digits + 10]; RealDigits[F'[rho], 10, digits] // First
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|