login
A099306
n''', the third arithmetic derivative of n.
11
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 12 2004
STATUS
approved