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 A099306 n''', the third arithmetic derivative of n. 10
 0, 0, 0, 0, 4, 0, 0, 0, 32, 1, 0, 0, 80, 0, 5, 16, 176, 0, 7, 0, 48, 1, 0, 0, 112, 1, 12, 27, 176, 0, 0, 0, 368, 6, 0, 32, 96, 0, 7, 80, 156, 0, 0, 0, 240, 32, 7, 0, 608, 6, 16, 44, 96, 0, 216, 80, 272, 1, 0, 0, 272, 0, 9, 24, 2368, 10, 0, 0, 220, 8, 0, 0, 284, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS For prime p, a(p^p) = p^p. a(A157037(n)) = 0. - Reinhard Zumkeller, Feb 22 2009 REFERENCES See A003415. LINKS T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 2000 terms from T. D. Noe) FORMULA a(n) = A003415(A003415(A003415(n))). MATHEMATICA dn[0]=0; dn[1]=0; dn[n_]:=Module[{f=Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus@@(n*f[[2]]/f[[1]])]]; Table[dn[dn[dn[n]]], {n, 100}] CROSSREFS Cf. A003415 (arithmetic derivative of n), A068346 (second arithmetic derivative of n), A099307 (least k such that the k-th arithmetic derivative of n is zero). Column k=3 of A258651. Sequence in context: A169765 A169768 A057386 * A228630 A174647 A258644 Adjacent sequences:  A099303 A099304 A099305 * A099307 A099308 A099309 KEYWORD nonn AUTHOR T. D. Noe, Oct 12 2004 STATUS approved

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Last modified April 19 08:15 EDT 2021. Contains 343110 sequences. (Running on oeis4.)