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 A074754 #25 Apr 18 2025 09:57:13
%S A074754 1,1,2,2,1,3,2,3,2,1,1,6,2,3,3,3,1,5,1,3,3,1,1,10,1,2,2,5,1,5,3,5,2,1,
%T A074754 2,9,1,2,4,5,1,8,1,3,3,1,1,13,2,1,2,3,1,7,1,8,3,1,1,12,1,4,4,5,2,3,1,
%U A074754 3,2,3,1,18,1,2,3,3,2,6,1,7,2,1,1,15,1,1,2,4,1,10,4,2,5,1,1,19,1,5,2,3,1
%N A074754 Number of integers k such that sigma(k) divides n.
%H A074754 Antti Karttunen, <a href="/A074754/b074754.txt">Table of n, a(n) for n = 1..16384</a>
%H A074754 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%H A074754 Amiram Eldar, <a href="/A074754/a074754.jpg">Plot of Sum_{k=1..n} a(k)/(n*log(n)) for n = 10^(1..7)</a>.
%H A074754 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A074754 Sum_{k=1..n} a(k) seems to be asymptotic to c*n*log(n) with c = 0.7...
%F A074754 G.f.: sum(k>=1, 1/(1-x^sigma(k))).
%F A074754 a(n) = Sum_{k=1..n} (1 - ceiling(n/sigma(k)) + floor(n/sigma(k))). - _Wesley Ivan Hurt_, Apr 21 2023
%t A074754 Table[Length[Select[Range[n], Divisible[n, DivisorSigma[1,#]]&]], {n, 1, 100}] (* _Vaclav Kotesovec_, Feb 16 2019 *)
%o A074754 (PARI) a(n)=sum(i=1,n,if(n%sigma(i),0,1))
%o A074754 (PARI) a(n)=if(n<1,0,polcoeff(sum(k=1,n,1/(1-x^sigma(k)),x*O(x^sigma(n))),n))
%o A074754 (PARI) a(n) = {my(s = []); fordiv(n, d, s = setunion(s, invsigma(d))); #s;} \\ _Amiram Eldar_, Apr 18 2025, using _Max Alekseyev_'s invphi.gp (see links).
%Y A074754 Cf. A000203, A070610.
%Y A074754 Row lengths of A378912.
%K A074754 nonn
%O A074754 1,3
%A A074754 _Benoit Cloitre_, Sep 28 2002