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%I #6 May 28 2017 09:14:06
%S 0,1,1,1,1,4,1,4,1,4,1,5,1,4,4,1,1,5,1,5,4,4,1,12,1,4,4,5,1,12,1,5,4,
%T 4,4,6,1,4,4,12,1,12,1,5,5,4,1,7,1,5,4,5,1,12,4,12,4,4,1,16,1,4,5,1,4,
%U 12,1,5,4,12,1,16,1,4,5,5,4,12,1,7,1,4,1,16,4,4,4,12,1,16,4,5,4,4,4,16,1,5
%N Arithmetic derivative of d(n), the number of divisors of n.
%D See A003415.
%H Antti Karttunen, <a href="/A099301/b099301.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A003415(A000005(n)).
%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[dn[DivisorSigma[0, n]], {n, 150}]
%Y Cf. A000005, A003415 (arithmetic derivative of n).
%K nonn
%O 1,6
%A _T. D. Noe_, Oct 12 2004
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