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%I #7 Jul 13 2013 12:03:16
%S 2,1,6,2,10,3,14,4,18,5,14,6,26,7,30,8,34,9,38,10,42,11,46,12,50,13,
%T 54,14,26,15,62,16,42,17,4,18,74,19,78,20,82,21,86,22,90,23,38,24,98,
%U 25,102,26,106,27,27,28,114,29,118,30,122,31,126,32,130,33,18,34,138,8,142
%N Least k > 0 such that (n+k)' = n' + k', where n' denotes the arithmetic derivative of n.
%C 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.
%D See A003415
%H Reinhard Zumkeller, <a href="/A099304/b099304.txt">Table of n, a(n) for n = 1..10000</a>
%t 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}]
%o (Haskell)
%o import Data.List (find)
%o import Data.Maybe (fromJust)
%o a099304 n = succ $ fromJust $ elemIndex 0 $
%o zipWith (-) (drop (fromInteger n + 1) a003415_list)
%o (map (+ n') $ tail a003415_list)
%o where n' = a003415 n
%o -- _Reinhard Zumkeller_, May 09 2011
%Y Cf. A003415 (arithmetic derivative of n), A099305 (number of solutions to (n+k)' = n' + k').
%K nonn
%O 1,1
%A _T. D. Noe_, Oct 12 2004
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