

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
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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



