OFFSET
1,1
COMMENTS
The arithmetic derivative does not, in general, have the linearity property. In most cases, a(n) = n/2 for even n and a(n) = 2n for odd n.
REFERENCES
See A003415
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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[k=1; While[dn[n]+dn[k] != dn[n+k], k++ ]; k, {n, 100}]
PROG
(Haskell)
import Data.List (find)
import Data.Maybe (fromJust)
a099304 n = succ $ fromJust $ elemIndex 0 $
zipWith (-) (drop (fromInteger n + 1) a003415_list)
(map (+ n') $ tail a003415_list)
where n' = a003415 n
-- Reinhard Zumkeller, May 09 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 12 2004
STATUS
approved