%I #18 Jun 12 2022 22:52:03
%S 1,9,441,815409,553613841
%N Integer solutions of the arithmetic differential equation m' = m - sqrt(m).
%C a(6) > 10^17. - _Giovanni Resta_, Mar 20 2014
%C m = k^2, where k satisfies k' = (k-1)/2. - _Charlie Neder_, Mar 08 2019
%e For m = 441 we have that m' = 420, sqrt(441) = 21 and 420 = 441 - 21.
%p with(numtheory); P:= proc(q) local n,p,x;
%p for n from 1 to q do x:=n^2;
%p if x*add(op(2,p)/op(1,p),p=ifactors(x)[2])=n^2-n then print(n^2);
%p fi; od; end: P(10^9);
%Y Cf. A003415, A239478.
%K nonn,more
%O 1,2
%A _Paolo P. Lava_, Mar 20 2014