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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 (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 December 5 19:19 EST 2016. Contains 278770 sequences.