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%I #9 Nov 29 2019 20:51:21
%S 81,108,216,540,1188,2484,5076,10260,23112,57996,135648,475632,
%T 1586736,4760640,20409408,89259840,374899968,1880140032,9400707072,
%U 64402394112,395614900224,2769304412160,22930714939392,162970999640064,1188480788434944,8320496444780544
%N The n-th arithmetic derivative of 3^4.
%C In general, the trajectory of p^(p+1) under A003415 is equal to p^p times the trajectory of p under A129283: n -> n + n'. Here we have the case p = 3 (see A129285 for a(n)/3^3), see A129150 and A129152 for p = 2 and 5. - _M. F. Hasler_, Nov 28 2019
%F a(n+1) = A003415(a(n)), a(0) = 3^4 = 81.
%F a(n) = A129285(n)*3^3; A129251(a(n)) > 0. - _Reinhard Zumkeller_, Apr 07 2007
%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 = 3^4; Join[{s}, Table[s = dn[s], {25}]] (* _T. D. Noe_, Mar 07 2013 *)
%o (Haskell)
%o a129151 n = a129151_list !! n
%o a129151_list = iterate a003415 81 -- _Reinhard Zumkeller_, Apr 29 2012
%Y Cf. A129150, A129152, A068327.
%Y Cf. A099309, A051674, A100716.
%K nonn
%O 0,1
%A _Reinhard Zumkeller_, Apr 01 2007
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