A099306 n''', the third arithmetic derivative of n.

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

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

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