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A304110 a(n) is the number of terms of A304107 <= n; Partial sums of A304109.

%I A304110 #8 May 13 2018 20:45:10
%S A304110 1,2,3,3,3,4,5,5,6,6,7,7,8,9,9,9,9,10,11,11,11,12,13,13,14,15,15,15,
%T A304110 16,16,17,17,18,18,19,19,20,21,21,21,22,22,23,23,23,24,25,25,26,27,27,
%U A304110 27,28,28,29,29,29,30,31,31,32,33,33,33,33,34,35,35,35,36,37,37,38,39,39,39,40,40,41,41,41,42,43,43,43,44
%N A304110 a(n) is the number of terms of A304107 <= n; Partial sums of A304109.
%C A304110 Question: Does lim_{n -> inf} a(n)/n converge to 1/2 ? See also A304111.
%H A304110 Antti Karttunen, <a href="/A304110/b304110.txt">Table of n, a(n) for n = 1..16384</a>
%H A304110 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%F A304110 a(1) = 1; for n > 1, a(n) = A304109(n) + a(n-1).
%o A304110 (PARI)
%o A304110 up_to = 128;
%o A304110 A304109(n) = { my(fm=factor(Pol(binary(n))*Mod(1, 2))); for(k=1, #fm~, if(fm[k, 2] > 1, return(0))); (1); };
%o A304110 prepare_v304110(up_to) = { my(v=vector(up_to), c=0); for(n=1, up_to, c += A304109(n); v[n] = c); (v); };
%o A304110 v304110 = prepare_v304110(up_to);
%o A304110 A304110(n) = v304110[n];
%Y A304110 Cf. A304107, A304109, A304111.
%K A304110 nonn
%O A304110 1,2
%A A304110 _Antti Karttunen_, May 13 2018