A281745 Numbers k with the property that the square root of the product of the digits of k is equal to the sum of the square roots of its digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 44, 149, 194, 228, 282, 333, 419, 491, 822, 914, 941, 11199, 11444, 11919, 11991, 14144, 14414, 14441, 19119, 19191, 19911, 41144, 41414, 41441, 44114, 44141, 44411, 91119, 91191, 91911, 99111, 11111449, 11111494, 11111944, 11114149

Offset: 1

Author

José de Jesús Camacho Medina, Jan 28 2017

Keywords

• nonn
• base

Examples

			    1 is a term because     sqrt(1) = sqrt(1);
   44 is a term because   sqrt(4*4) = sqrt(4) + sqrt(4);
  941 is a term because sqrt(9*4*1) = sqrt(9) + sqrt(4) + sqrt(1).
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A007954, A034710.

Programs

Mathematica

Select[Range[10^6], Sqrt[Times @@ #] == Total[Sqrt@ #] &@ IntegerDigits@ # &] (* Michael De Vlieger, Feb 02 2017 *)

PARI

isok(n) = my(d = vecsort(digits(n))); sqrt(prod(k=1, #d, d[k])) == sum(k=1, #d, sqrt(d[k])); \\ Michel Marcus, Jan 29 2017

Extensions

More terms from Jon E. Schoenfield, Jan 30 2017