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A242977
Decimal expansion of Sum_{k>1} 1/(k*(k-1)*zeta(k)), a constant related to Niven's constant.
2
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
0,1
COMMENTS
The asymptotic mean of the reciprocals of the maximal exponent in prime factorization of the positive integers. - Amiram Eldar, Dec 15 2022
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.
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
EXAMPLE
0.766944490521088241652417923...
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
PROG
(PARI) sumpos(k = 2, 1/(k*(k-1)*zeta(k))) \\ Amiram Eldar, Dec 15 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved