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%I #11 Oct 12 2021 21:58:00
%S 0,4,12,6,32,10,27,80,60,14,192,156,108,140,216,22,75,448,384,26,252,
%T 380,540,240,405,1024,912,34,756,147,38,700,960,1296,420,572,800,2304,
%U 46,2112,500,1836,945,780,1458,1792,2320,58,3024,1860,62,1628,2592
%N Arithmetic derivative of powerful numbers, cf. A001694.
%H Reinhard Zumkeller, <a href="/A258565/b258565.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A003415(A001694(n)).
%t ader[n_] := Switch[n, 0|1, 0, _, If[PrimeQ[n], 1, Sum[Module[{p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]];
%t ader /@ Join[{1}, Select[Range[1000], AllTrue[FactorInteger[#][[All, 2]], # > 1&]&]] (* _Jean-François Alcover_, Oct 12 2021 *)
%o (Haskell)
%o a258565 = a003415 . a001694
%Y Cf. A003415, A001694, A068720, A068328, A078310.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Jun 03 2015