This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A343224 #15 Dec 29 2024 04:08:01
%S A343224 1,2,3,3,5,7,7,3,7,11,11,12,13,15,16,-1,17,18,19,18,22,23,23,16,21,27,
%T A343224 13,24,29,41,31,-17,34,35,36,31,37,39,40,22,41,55,43,36,39,47,47,12,
%U A343224 43,48,52,42,53,39,56,28,58,59,59,76,61,63,53,-65,66,83,67,54,70,85,71,39,73,75,69,60,78,97,79,10,13
%N A343224 a(n) = sigma(n) - A003415(n), where A003415 is the arithmetic derivative, and sigma is the sum of divisors of n.
%H A343224 Antti Karttunen, <a href="/A343224/b343224.txt">Table of n, a(n) for n = 1..20000</a>
%H A343224 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A343224 a(n) = A000203(n) - A003415(n).
%F A343224 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Pi^2/6 - Sum_{p prime} 1/(p*(p-1)) = A013661 - A136141 = 0.871777... . - _Amiram Eldar_, Dec 29 2024
%o A343224 (PARI)
%o A343224 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A343224 A343224(n) = sigma(n) - A003415(n);
%Y A343224 Cf. A000203, A003415, A013661, A136141.
%K A343224 sign
%O A343224 1,2
%A A343224 _Antti Karttunen_, Apr 15 2021