%I #11 May 28 2017 09:35:11
%S 2,4,12,160,1255,256,12279,3072,1113823,119120,2191040,4640768,
%T 1835008,12805120,134217728
%N Least numbers k > 1 such that k'' = n*k', where k' and k'' are the first and the second arithmetic derivatives of k.
%e a(3) = 160 because 160'' / 160' = 1296 / 432 = 3 and this is the least number to have this property.
%p with(numtheory): P:=proc(q) local a,b,k,n,p; for n from 0 to q do
%p for k from 2 to q do a:=k*add(op(2,p)/op(1,p),p=ifactors(k)[2]); b:=a*add(op(2,p)/op(1,p),p=ifactors(a)[2]); if b=n*a then print(k); break;
%p fi; od; od; end: P(10^9);
%Y Cf. A003415, A068346.
%K nonn,more
%O 0,1
%A _Paolo P. Lava_, May 19 2017
