TOPICS
Search

Feller-Tornier Constant

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook

The Feller-Tornier constant is the density of integers that have an even number of prime factors p_i^(a_i) with a_1>1 in their prime factorization. It is given by

C_(Feller-Tornier)=1/2+1/2product_(n=1)^(infty)(1-2/(p_n^2))
(1)
=0.6613170494...
(2)

(OEIS A065493), where p_n is the nth prime. It can be given by the sum

C_(Feller-Tornier)=1/2{1+exp[-sum_(n=1)^infty(2^nP(n))/n]},
(3)

where P(n) is the prime zeta function.

See also

Artin's Constant, Barban's Constant, Heath-Brown-Moroz Constant, Murata's Constant, Prime Products, Quadratic Class Number Constant, Sarnak's Constant, Squarefree, Taniguchi's Constant, Twin Primes Constant

Explore with Wolfram|Alpha

References

Cohen, E. "Some Asymptotic Formulas in the Theory of Numbers." Trans. Amer. Math. Soc. 112, 214-227, 1964.Feller, W. and Tornier, E. "Mengentheoretische Untersuchungen von Eigenschaften der Zahlenreihe." Math. Ann. 107, 188-232, 1933.Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, p. 106, 2003.Niklasch, G. "Some Number-Theoretical Constants." http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml.Schoenberg, I. J. "On Asymptotic Distributions of Arithmetical Functions." Trans. Amer. Math. Soc. 39, 315-330, 1936.Sloane, N. J. A. Sequence A065493 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Feller-Tornier Constant

Cite this as:

Weisstein, Eric W. "Feller-Tornier Constant." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Feller-TornierConstant.html

Subject classifications