A214800 The n-th arithmetic derivative of 4^5.

1024, 5120, 26624, 148480, 777216, 4249600, 25123840, 134268928, 741121024, 3811486720, 19819736064, 112733967360, 644174359552, 3220871798784, 22009290649600, 142032743280640, 881678229782528, 6174273912848384, 44101956520460288, 312415523110846464

Offset: 0

Author

Franz Tolosa, Mar 07 2013

Keywords

• nonn

Comments

See A003415 for the definition of the arithmetic derivative.

Crossrefs

Cf. A003415, A129150, A129151, A129152.

Programs

Mathematica

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 *)