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A380267 a(n) is the denominator of the mean value of A051904(k) at the range k = 1..n.

%I A380267 #10 Feb 16 2025 08:34:07
%S A380267 1,2,3,1,1,1,1,4,3,10,11,4,13,14,5,8,17,3,19,10,7,11,23,4,25,26,3,28,
%T A380267 29,10,31,32,33,34,35,18,37,19,39,20,41,3,43,22,45,23,47,24,49,10,17,
%U A380267 52,53,18,11,56,19,58,59,4,61,62,21,16,13,33,67,17,69,7
%N A380267 a(n) is the denominator of the mean value of A051904(k) at the range k = 1..n.
%H A380267 Amiram Eldar, <a href="/A380267/b380267.txt">Table of n, a(n) for n = 1..10000</a>
%H A380267 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 A380267 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>.
%H A380267 Wikipedia, <a href="https://en.wikipedia.org/wiki/Niven%27s_constant">Niven's constant</a>.
%F A380267 a(n) = denominator((Sum_{k=1..n} A051904(k))/n).
%t A380267 f[n_] := Min[FactorInteger[n][[;;, 2]]]; f[1] = 0; With[{m = 100}, Denominator[Accumulate[Array[f, m]] / Range[m]]]
%o A380267 (PARI) lista(nmax) = {my(s = 0); print1(1, ", "); for(n = 2, nmax, s += vecmin(factor(n)[,2]);  print1(denominator(s/n), ", "));}
%Y A380267 Cf. A051904, A380266 (numerators).
%K A380267 nonn,easy,frac
%O A380267 1,2
%A A380267 _Amiram Eldar_, Jan 18 2025