A129151 The n-th arithmetic derivative of 3^4.

81, 108, 216, 540, 1188, 2484, 5076, 10260, 23112, 57996, 135648, 475632, 1586736, 4760640, 20409408, 89259840, 374899968, 1880140032, 9400707072, 64402394112, 395614900224, 2769304412160, 22930714939392, 162970999640064, 1188480788434944, 8320496444780544

Offset: 0

Author

Reinhard Zumkeller, Apr 01 2007

Keywords

• nonn

Comments

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

Crossrefs

Cf. A129150, A129152, A068327.

Cf. A099309, A051674, A100716.

Programs

Haskell

a129151 n = a129151_list !! n
a129151_list = iterate a003415 81  -- Reinhard Zumkeller, Apr 29 2012

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 = 3^4; Join[{s}, Table[s = dn[s], {25}]] (* T. D. Noe, Mar 07 2013 *)

Formula

a(n+1) = A003415(a(n)), a(0) = 3^4 = 81.

a(n) = A129285(n)*3^3; A129251(a(n)) > 0. - Reinhard Zumkeller, Apr 07 2007