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 A068721 #16 Apr 11 2025 03:31:45 %S A068721 0,12,27,192,75,540,147,2304,1458,2100,363,6912,507,5292,5400,24576, %T A068721 867,20412,1083,28800,13230,18876,1587,76032,18750,30420,59049,75264, %U A068721 2523,83700,2883,245760,45738,65892,44100 %N A068721 Arithmetic derivative of cubes: a(n) = 3*n^2*A003415(n). %H A068721 Bruno Berselli, <a href="/A068721/b068721.txt">Table of n, a(n) for n = 1..1000</a> %F A068721 a(n) = A003415(A000578(n)). %t A068721 ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad[0] = ad[1] = 0; a[n_] := 3 * n^2 * ad[n]; Array[a, 100] (* _Amiram Eldar_, Apr 11 2025 *) %o A068721 (Magma) Ad:=func<h | h*(&+[Factorisation(h)[i][2]/Factorisation(h)[i][1]: i in [1..#Factorisation(h)]])>; [0] cat [Ad(n^3): n in [2..40]]; // _Bruno Berselli_, Oct 22 2013 %o A068721 (Python) %o A068721 from sympy import factorint %o A068721 def A068721(n): return 3*n**2*sum((n*e//p for p,e in factorint(n).items())) if n > 1 else 0 # _Chai Wah Wu_, Nov 03 2022 %Y A068721 Cf. A000578, A003415, A068720. %K A068721 nonn,easy %O A068721 1,2 %A A068721 _Reinhard Zumkeller_, Feb 26 2002