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A157104 Arithmetic derivative of cubefree numbers. 1

%I #10 May 05 2017 10:56:38

%S 0,1,1,4,1,5,1,6,7,1,16,1,9,8,1,21,1,24,10,13,1,10,15,32,1,31,1,14,19,

%T 12,60,1,21,16,1,41,1,48,39,25,1,14,45,20,56,1,16,22,31,1,92,1,33,51,

%U 18,61,1,72,26,59,1,1,39,55,80,18,71,1,43,1,124,22,45,32,1,123,20,96,34,49

%N Arithmetic derivative of cubefree numbers.

%C a(n) = A003415(A004709(n)).

%H Reinhard Zumkeller, <a href="/A157104/b157104.txt">Table of n, a(n) for n = 1..10000</a>

%t Reap[Do[f = FactorInteger[n]; If[n == 1, Sow[0], If[And @@ (# <= 2 & ) /@ f[[All, 2]], Sow[Total[n*(f[[All, 2]]/f[[All, 1]])]]]], {n, 1, 100}]][[2, 1]] (* _Jean-François Alcover_, May 16 2013 *)

%o (Haskell)

%o a157104 = a003415 . a004709 -- _Reinhard Zumkeller_, May 24 2013

%Y Cf. A068328, A068720.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Feb 23 2009

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