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A129151
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The n-th arithmetic derivative of 3^4.
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9
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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FORMULA
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a(n+1) = A003415(a(n)), a(0) = 3^4 = 81.
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a129151 n = a129151_list !! n
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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