cp's OEIS Frontend

A380264 a(n) is the numerator of the mean value of A051903(k) at the range k = 1..n.

%I A380264 #11 Feb 16 2025 08:34:07
%S A380264 0,1,2,1,1,1,1,5,4,13,14,4,17,9,19,23,24,13,27,29,10,31,32,35,37,19,
%T A380264 41,43,44,3,46,51,52,53,54,14,57,29,59,31,63,32,65,67,23,35,71,25,11,
%U A380264 79,80,41,83,43,87,45,91,46,93,19,96,97,11,105,106,107,108,55
%N A380264 a(n) is the numerator of the mean value of A051903(k) at the range k = 1..n.
%H A380264 Amiram Eldar, <a href="/A380264/b380264.txt">Table of n, a(n) for n = 1..10000</a>
%H A380264 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 A380264 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NivensConstant.html">Niven's Constant</a>.
%H A380264 Wikipedia, <a href="https://en.wikipedia.org/wiki/Niven%27s_constant">Niven's constant</a>.
%F A380264 a(n) = numerator((Sum_{k=1..n} A051903(k))/n).
%F A380264 a(n)/A380265(n) = A129132(n)/n.
%F A380264 Limit_{n->oo} a(n)/A380265(n) = c, where c is Niven's constant (A033150).
%F A380264 abs(a(n)/A380265(n) - c) <= 3*log_2(n)/sqrt(n).
%e A380264 Fractions begin with 0, 1/2, 2/3, 1, 1, 1, 1, 5/4, 4/3, 13/10, 14/11, 4/3, ...
%t A380264 f[n_] := Max[FactorInteger[n][[;;, 2]]]; f[1] = 0; With[{m = 100}, Numerator[Accumulate[Array[f, m]] / Range[m]]]
%o A380264 (PARI) lista(nmax) = {my(s = 0); print1(0, ", "); for(n = 2, nmax, s += vecmax(factor(n)[,2]);  print1(numerator(s/n), ", "));}
%Y A380264 Cf. A033150, A051903, A129132, A359071, A359072, A380265 (denominators).
%K A380264 nonn,easy,frac
%O A380264 1,3
%A A380264 _Amiram Eldar_, Jan 18 2025