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

1,2

Links

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

Example

    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).

Mathematica

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

Prog

(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

Crossrefs

Cf. A007953, A007954, A034710.

Sequence in context: A342442 A342755 A129513 * A302501 A183532 A257829

Adjacent sequences: A281742 A281743 A281744 * A281746 A281747 A281748

Keyword

nonn,base

Author

José de Jesús Camacho Medina, Jan 28 2017

Extensions

More terms from Jon E. Schoenfield, Jan 30 2017

Status

approved