A242977 Decimal expansion of Sum_{k>1} 1/(k*(k-1)*zeta(k)), a constant related to Niven's constant.
7, 6, 6, 9, 4, 4, 4, 9, 0, 5, 2, 1, 0, 8, 8, 2, 4, 1, 6, 5, 2, 4, 1, 7, 9, 2, 3, 0, 0, 3, 1, 7, 6, 9, 3, 0, 9, 7, 4, 7, 5, 7, 8, 8, 9, 9, 3, 1, 9, 0, 5, 1, 6, 9, 6, 5, 4, 1, 2, 2, 0, 8, 1, 6, 0, 7, 8, 9, 6, 8, 4, 2, 3, 7, 5, 6, 7, 9, 5, 7, 7, 5, 7, 8, 9, 3, 7, 4, 6, 2, 9, 8, 4, 0, 9, 9, 4, 3
Offset: 0
Examples
0.766944490521088241652417923...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.6 Niven's constant, p. 113.
Links
- Wolfgang Schwarz and Jürgen Spilker, A remark on some special arithmetical functions, in: E. Laurincikas , E. Manstavicius and V. Stakenas (eds.), Analytic and Probabilistic Methods in Number Theory, Proceedings of the Second International Conference in Honour of J. Kubilius, Palanga, Lithuania, 23-27 September 1996, New Trends in Probability and Statistics, Vol. 4, VSP BV & TEV Ltd. (1997), pp. 221-245.
- D. Suryanarayana and R. Sita Rama Chandra Rao, On the maximum and minimum exponents in factoring integers, Archiv der Mathematik, Vol. 28, No. 1 (1977), pp. 261-269.
- Eric Weisstein's World of Mathematics, Niven's Constant.
Programs
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Mathematica
digits = 98; m0 = 100; dm = 100; Clear[f]; f[m_] := f[m] = NSum[1/(k*(k - 1)*Zeta[k]), {k, 2, m}, WorkingPrecision -> digits + 10, NSumTerms -> m] + 1/m; f[m0]; f[m = m0 + dm]; While[RealDigits[f[m], 10, digits] != RealDigits[f[m - dm], 10, digits], Print["m = ", m ]; m = m + dm]; RealDigits[f[m], 10, digits] // First -
PARI
sumpos(k = 2, 1/(k*(k-1)*zeta(k))) \\ Amiram Eldar, Dec 15 2022
Formula
Equals lim_{n->oo} (1/n) * Sum_{k=2..n} 1/A051903(k). - Amiram Eldar, Oct 16 2020
Equals 1 + Sum_{k>=2} (1/zeta(k)-1)/(k*(k-1)). - Amiram Eldar, Dec 15 2022
Comments