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%I #15 Mar 08 2013 00:15:29
%S 1024,5120,26624,148480,777216,4249600,25123840,134268928,741121024,
%T 3811486720,19819736064,112733967360,644174359552,3220871798784,
%U 22009290649600,142032743280640,881678229782528,6174273912848384,44101956520460288,312415523110846464
%N The n-th arithmetic derivative of 4^5.
%C See A003415 for the definition of the arithmetic derivative.
%t dn[0] = 0; dn[1] = 0; dn[n_?Negative] := -dn[-n]; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Total[n*f[[2]]/f[[1]]]]]; s = 4^5; Join[{s}, Table[s = dn[s], {19}]] (* _T. D. Noe_, Mar 07 2013 *)
%Y Cf. A003415, A129150, A129151, A129152.
%K nonn
%O 0,1
%A _Franz Tolosa_, Mar 07 2013
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