%I #38 Apr 07 2016 02:53:32
%S 0,1,2704,5184,7744
%N Numbers of the form (pq)^2, where p is the number of digits of n (A055642) and q is the sum of the digits of n (A007953).
%e 2704 is a term because 2704 = [4*(2+7+0+4)]^2;
%e 5184 is a term because 5184 = [4*(5+1+8+4)]^2.
%t Position[ Table[ IntegerLength[k] Sum[( Floor[k/10^n] - 10 Floor[k/10^(n + 1)]), {n, 0, IntegerLength@ k^2}] - k, {k, 1, 10^6}], 0] // Flatten = {1, 1232, 4100, 268542}
%t Select[Range[10^3]^2,With[{id=IntegerDigits[#]},#==(Length[id]*Plus@@id)^2]&] (* _Ray Chandler_, Apr 01 2016 *)
%o (PARI) isok(n) = d = digits(n); (#d*vecsum(d))^2 == n; \\ _Michel Marcus_, Mar 26 2016
%Y Cf. A007953, A055642, A257784.
%K nonn,base,fini,full
%O 1,3
%A _José de Jesús Camacho Medina_, Mar 18 2016