%I #12 Apr 23 2017 23:59:34

%S 4,16,18,20,21,24,26,27,33,35,38,40,44,45,48,50,51,52,56,57,62,63,65,

%T 68,69,74,75,76,77,80,85,86,91,92,93,95,96,98,99,104,106,108,111,115,

%U 117,119,122,123,126,129,133,134,135,136,141,143,144,145,146,147

%N Numbers k such that A001221(k) = A001221(A003415(k)).

%C Numbers k such that the number of distinct prime divisors of k is equal to the number of distinct prime divisors of the arithmetic derivative of k.

%H Colin Barker, <a href="/A281685/b281685.txt">Table of n, a(n) for n = 1..1000</a>

%t a[n_] := If[Abs@n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[Abs@n]]];

%t Select[Range[100], PrimeNu[#] == PrimeNu[a[#]] &] (* _G. C. Greubel_, Apr 23 2017 *)

%o (PARI) arde(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i])

%o select(k->omega(k)==omega(arde(k)), vector(200, k, k+1))

%Y Cf. A001221, A003415, A209870, A281686.

%K nonn

%O 1,1

%A _Colin Barker_, Jan 27 2017