cp's OEIS Frontend

A387409 Partial sums of A387422 minus partial sums of A387412.

%I A387409 #21 Sep 03 2025 13:54:35
%S A387409 0,0,0,-2,-2,-1,-1,-1,-1,-3,-3,-2,-1,0,1,0,0,-1,-1,2,3,3,3,4,2,0,-1,2,
%T A387409 2,1,1,1,-3,-3,-5,-4,-2,-4,-5,-5,-5,-8,-8,-6,-7,-8,-8,-10,-10,-10,-10,
%U A387409 -8,-6,-5,-5,-3,-8,-8,-8,-8,-5,-5,-4,-5,-4,-2,-2,-3,-5,-3,-3,-4,-3,-3,-3,-1,-3,-2,-2,-1,-2,-3,-2
%N A387409 Partial sums of A387422 minus partial sums of A387412.
%C A387409 Also partial sums of A387413 minus partial sums of A387423.
%C A387409 This sequence gives some measure of how much longer the common prefix of the binary expansions of n and sigma(n) is - on average - than the common prefix of the binary expansions of n and A003961(n).
%C A387409 Question: Does the sequence eventually grow without limit and is it just because A003961(n) >= A000203(n)? Does ratio a(n)/n converge to any limit?
%H A387409 Antti Karttunen, <a href="/A387409/b387409.txt">Table of n, a(n) for n = 1..65537</a>
%H A387409 A. Karttunen, <a href="https://oeis.org/plot2a?name1=A387409&amp;name2=A000027&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=ratio&amp;drawpoints=true">Ratio a(n)/n, plotted with OEIS Plot2-tool</a>
%H A387409 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>.
%H A387409 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%H A387409 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A387409 a(n) = A387407(n) - A387408(n).
%F A387409 a(n) = A387425(n) - A387424(n).
%o A387409 (PARI) A387409(n) = (A387407(n) - A387408(n));
%Y A387409 Cf. A000203, A003961, A387407, A387408, A387412, A387413, A387422, A387423, A387424, A387425.
%K A387409 sign,base,new
%O A387409 1,4
%A A387409 _Antti Karttunen_, Sep 03 2025