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A273993 Numbers whose derivative is equal to the arithmetic derivative.

%I A273993 #16 Jun 17 2016 02:22:02
%S A273993 0,1,2,10,22,34,38,46,94,134,142,158,262,382,514,526,542,766,2062,
%T A273993 2078,2174,2302,2558,4126,4222,7871,8198,8222,8254,8318,10238,12286,
%U A273993 16894,32894,40958,65542,65566,65662,66046,67582,131074,131078,131086,131102,131198,132094
%N A273993 Numbers whose derivative is equal to the arithmetic derivative.
%H A273993 Paolo P. Lava, <a href="/A273993/b273993.txt">Table of n, a(n) for n = 1..78</a>
%F A273993 Solution of the equation A003415(n) = A038554(n).
%e A273993 10 in base 2 is 1010 and its derivative is (1+0)(0+1)(1+0)-> 111 that is 7 in base 10 and 7 is also the arithmetic derivative of 10.
%p A273993 with(numtheory): P:=proc(q) local a,b,i,n,p;
%p A273993 for n from 0 to q do a:=0; b:=convert(n,base,2);
%p A273993 for i from 1 to nops(b)-1 do a:=a+((b[i]+b[i+1]) mod 2)*2^(i-1); od;
%p A273993 if a=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]) then print(n); fi;
%p A273993 od; end: P(10^6);
%Y A273993 Cf. A003415, A038554, A274073.
%K A273993 nonn,easy
%O A273993 1,3
%A A273993 _Paolo P. Lava_, Jun 08 2016