A033150 Decimal expansion of Niven's constant.
1, 7, 0, 5, 2, 1, 1, 1, 4, 0, 1, 0, 5, 3, 6, 7, 7, 6, 4, 2, 8, 8, 5, 5, 1, 4, 5, 3, 4, 3, 4, 5, 0, 8, 1, 6, 0, 7, 6, 2, 0, 2, 7, 6, 5, 1, 6, 5, 3, 4, 6, 9, 0, 9, 9, 9, 9, 4, 2, 8, 4, 9, 0, 6, 5, 4, 7, 3, 1, 3, 1, 9, 2, 1, 6, 8, 1, 2, 2, 4, 9, 1, 9, 3, 4, 2, 4, 4, 1, 3, 2, 1, 0, 0, 8, 7, 1, 0, 0, 1, 7, 9
Offset: 1
Examples
1.7052111401...
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.
Programs
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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 *) -
PARI
1+suminf(j=2,1-1/zeta(j)) \\ Charles R Greathouse IV, Aug 13 2017
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
Extensions
Offset corrected by Oleg Marichev (oleg(AT)wolfram.com), Jan 28 2008
Comments