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 A336465 #15 Sep 09 2023 14:50:21
%S A336465 1,2,3,6,5,6,7,12,12,10,11,18,13,14,15,24,17,24,19,30,21,22,23,36,30,
%T A336465 26,36,42,29,30,31,48,33,34,35,72,37,38,39,60,41,42,43,66,60,46,47,72,
%U A336465 56,60,51,78,53,72,55,84,57,58,59,90,61,62,84,96,65,66,67,102,69,70,71,108,73,74,90,114,77,78,79,120
%N A336465 Recursive variant of A057723: If n is cubefree, then a(n) = A057723(n), otherwise a(n) = A007947(n) * a(n/A007947(n)).
%C A336465 Not multiplicative. The least counterexample is 72 = 8*9: a(72) = 108, while a(8) * a(9) = 12 * 12 = 144. - _Amiram Eldar_, Sep 09 2023
%H A336465 Antti Karttunen, <a href="/A336465/b336465.txt">Table of n, a(n) for n = 1..16384</a>
%H A336465 Antti Karttunen, <a href="/A336465/a336465.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A336465 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A336465 a(n) = Sum_{k=1..n} (1 - ceiling(n/k^2) + floor(n/k^2)) * mu(k)^2 * (n/k), where mu is the Möbius function (A008683). - _Wesley Ivan Hurt_, Jan 29 2021
%t A336465 f[p_, e_] := (p^(e + 1) - 1)/(p - 1) - 1; a[1] = 1; a[n_] := a[n] = Module[{fct = FactorInteger[n]}, If[Max[fct[[;; , 2]]] < 3, Times @@ f @@@ fct, r = Times @@ fct[[;; , 1]]; r*a[n/r]]]; Array[a, 100] (* _Amiram Eldar_, Sep 09 2023 *)
%o A336465 (PARI) A336465(n) = if(issquarefree(n), n, my(f=factor(n), r=factorback(f[,1])); if(issquarefree(n/r),r*sigma(n/r),r*A336465(n/r)));
%Y A336465 Cf. A000203, A007947, A057723.
%K A336465 nonn
%O A336465 1,2
%A A336465 _Antti Karttunen_, Jul 31 2020
%E A336465 Keyword mult removed by _Amiram Eldar_, Sep 09 2023