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A380266 a(n) is the numerator of the mean value of A051904(k) at the range k = 1..n.

%I A380266 #9 Feb 16 2025 08:34:07
%S A380266 0,1,2,1,1,1,1,5,4,13,14,5,16,17,6,11,23,4,25,13,9,14,29,5,32,33,4,37,
%T A380266 38,13,40,45,46,47,48,25,51,26,53,27,55,4,57,29,59,30,61,31,64,13,22,
%U A380266 67,68,23,14,71,24,73,74,5,76,77,26,21,17,43,87,22,89,9
%N A380266 a(n) is the numerator of the mean value of A051904(k) at the range k = 1..n.
%H A380266 Amiram Eldar, <a href="/A380266/b380266.txt">Table of n, a(n) for n = 1..10000</a>
%H A380266 Ivan Niven, <a href="https://doi.org/10.1090/S0002-9939-1969-0241373-5">Averages of Exponents in Factoring Integers</a>, Proc. Amer. Math. Soc., Vol. 22, No. 2 (1969), pp. 356-360.
%H A380266 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>.
%H A380266 Wikipedia, <a href="https://en.wikipedia.org/wiki/Niven%27s_constant">Niven's constant</a>.
%F A380266 a(n) = numerator((Sum_{k=1..n} A051904(k))/n).
%F A380266 a(n)/A380267(n) = 1 + c/sqrt(n) + o(1/sqrt(n)), where c = zeta(3/2)/zeta(3) (A090699).
%e A380266 Fractions begin with 0, 1/2, 2/3, 1, 1, 1, 1, 5/4, 4/3, 13/10, 14/11, 5/4, ...
%t A380266 f[n_] := Min[FactorInteger[n][[;;, 2]]]; f[1] = 0; With[{m = 100}, Numerator[Accumulate[Array[f, m]] / Range[m]]]
%o A380266 (PARI) lista(nmax) = {my(s = 0); print1(0, ", "); for(n = 2, nmax, s += vecmin(factor(n)[,2]);  print1(numerator(s/n), ", "));}
%Y A380266 Cf. A051904, A090699, A380267 (denominators).
%K A380266 nonn,easy,frac
%O A380266 1,3
%A A380266 _Amiram Eldar_, Jan 18 2025