|
|
A083342
|
|
Decimal expansion of average deviation of the total number of prime factors.
|
|
10
|
|
|
1, 0, 3, 4, 6, 5, 3, 8, 8, 1, 8, 9, 7, 4, 3, 7, 9, 1, 1, 6, 1, 9, 7, 9, 4, 2, 9, 8, 4, 6, 4, 6, 3, 8, 2, 5, 4, 6, 7, 0, 3, 0, 7, 9, 8, 4, 3, 4, 4, 3, 8, 5, 2, 5, 4, 5, 0, 3, 0, 7, 0, 2, 8, 1, 2, 8, 1, 6, 3, 3, 5, 3, 9, 3, 8, 6, 6, 0, 1, 6, 0, 7, 5, 4, 7, 9, 4, 1, 3, 9, 0, 2, 5, 7, 5, 6, 7, 4, 6, 9, 3, 8
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Or, decimal expansion of constant B2 from the summatory function of the restricted divisor function.
The constant A in the asymptotic formula Sum_{prime p <= n} 1/(p-1) = log(log(n)) + A + O(1/log(n)) (Jakimczuk, 2017). - Amiram Eldar, Mar 18 2024
|
|
REFERENCES
|
Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, Vol. 94, Cambridge University Press, 2003, pp. 94-98.
József Sándor and Borislav Crstici, Handbook of Number Theory II, Kluwer Academic Publishers, 2004, p. 155, Chapter V, 1) b).
|
|
LINKS
|
|
|
FORMULA
|
Equals gamma + Sum_{p prime} (log(1-1/p) + 1/(p-1)), where gamma is Euler's constant (A001620). - Amiram Eldar, Dec 25 2021
Equals gamma + Sum_{k>=2} phi(k) * log(zeta(k)) / k, where phi = A000010.
Equals gamma - Sum_{p prime} 1/(p-1)^2 + Sum_{k>=2} J_2(k) * log(zeta(k)) / k, where J_2 = A007434.
Both formulas are from Jakimczuk (2017). (End)
|
|
EXAMPLE
|
1.03465388189743791161979429846463825467030798434438525450307...
|
|
MATHEMATICA
|
digits = 102; Mp = EulerGamma - NSum[PrimeZetaP[n]/n - PrimeZetaP[n], {n, 2, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 3*digits]; RealDigits[Mp, 10, digits] // First (* Jean-François Alcover, Sep 02 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|