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%I #11 Nov 03 2022 11:23:07
%S 0,12,27,192,75,540,147,2304,1458,2100,363,6912,507,5292,5400,24576,
%T 867,20412,1083,28800,13230,18876,1587,76032,18750,30420,59049,75264,
%U 2523,83700,2883,245760,45738,65892,44100
%N Arithmetic derivative of cubes: a(n) = 3*n^2*A003415(n).
%H Bruno Berselli, <a href="/A068721/b068721.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A003415(A000578(n)).
%o (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 (Python)
%o from sympy import factorint
%o 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 Cf. A068720, A000578, A003415.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Feb 26 2002
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