This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A242977 #24 Feb 16 2025 08:33:22
%S A242977 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,
%T A242977 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,
%U A242977 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
%N A242977 Decimal expansion of Sum_{k>1} 1/(k*(k-1)*zeta(k)), a constant related to Niven's constant.
%C A242977 The asymptotic mean of the reciprocals of the maximal exponent in prime factorization of the positive integers. - _Amiram Eldar_, Dec 15 2022
%D A242977 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.6 Niven's constant, p. 113.
%H A242977 Wolfgang Schwarz and Jürgen Spilker, <a href="https://doi.org/10.1515/9783110944648.221">A remark on some special arithmetical functions</a>, 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.
%H A242977 D. Suryanarayana and R. Sita Rama Chandra Rao, <a href="https://doi.org/10.1007/BF01223919">On the maximum and minimum exponents in factoring integers</a>, Archiv der Mathematik, Vol. 28, No. 1 (1977), pp. 261-269.
%H A242977 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>.
%F A242977 Equals lim_{n->oo} (1/n) * Sum_{k=2..n} 1/A051903(k). - _Amiram Eldar_, Oct 16 2020
%F A242977 Equals 1 + Sum_{k>=2} (1/zeta(k)-1)/(k*(k-1)). - _Amiram Eldar_, Dec 15 2022
%e A242977 0.766944490521088241652417923...
%t A242977 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
%o A242977 (PARI) sumpos(k = 2, 1/(k*(k-1)*zeta(k))) \\ _Amiram Eldar_, Dec 15 2022
%Y A242977 Cf. A033150, A051903, A072102, A090699.
%K A242977 nonn,cons
%O A242977 0,1
%A A242977 _Jean-François Alcover_, May 28 2014