

A099306


n''', the third arithmetic derivative of n.


6



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
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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 kth 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



