OFFSET
1,2
COMMENTS
This constant is the average value of A051903. - Charles R Greathouse IV, Oct 30 2012
There are no 9's in the first 50 digits after the decimal point. Then, suddenly, it goes 909999. - Bobby Jacobs, Aug 13 2017
Named after the Canadian-American mathematician Ivan Morton Niven (1915 - 1999). - Amiram Eldar, Aug 19 2020
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 112-115.
LINKS
C. W. Anderson, Problem 6015, The American Mathematical Monthly, Vol. 82, No. 2 (1975), pp. 183-184, T. Salat, Prime Decomposition of Integers, solution to Problem 6015, ibid., Vol. 83, No. 10 (1976), p. 820.
Ivan Niven, Averages of Exponents in Factoring Integers, Proc. Amer. Math. Soc., Vol. 22, No. 2 (1969), pp. 356-360.
Simon Plouffe, The Niven constant to 256 digits.
Kaneenika Sinha, Average orders of certain arithmetical functions, Journal of the Ramanujan Mathematical Society, Vol. 21, No. 3 (2006), pp. 267-277.
Eric Weisstein's World of Mathematics, Niven's Constant.
Wikipedia, Niven's constant.
FORMULA
Equals 1 + Sum_{j>=2} 1-(1/zeta(j)).
Equals 1 - Sum_{k>=2} mu(k)/(k*(k-1)), where mu is the Möbius function (A008683) (Anderson, 1975; Sinha, 2006). - Amiram Eldar, Aug 19 2020
EXAMPLE
1.7052111401...
MATHEMATICA
rd[n_] := rd[n] = RealDigits[ N[1 + Sum[1 - 1/Zeta[j], {j, 2, 2^n}] , 105]][[1]]; rd[n = 4]; While[rd[n] =!= rd[n-1], n++]; rd[n] (* Jean-François Alcover, Oct 25 2012 *)
PROG
(PARI) 1+suminf(j=2, 1-1/zeta(j)) \\ Charles R Greathouse IV, Aug 13 2017
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
EXTENSIONS
Offset corrected by Oleg Marichev (oleg(AT)wolfram.com), Jan 28 2008
STATUS
approved