A281745 - OEIS

%I #31 Aug 14 2017 03:25:26

%S 1,2,3,4,5,6,7,8,9,44,149,194,228,282,333,419,491,822,914,941,11199,

%T 11444,11919,11991,14144,14414,14441,19119,19191,19911,41144,41414,

%U 41441,44114,44141,44411,91119,91191,91911,99111,11111449,11111494,11111944,11114149

%N 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.

%H Chai Wah Wu, <a href="/A281745/b281745.txt">Table of n, a(n) for n = 1..10000</a>

%e     1 is a term because     sqrt(1) = sqrt(1);

%e    44 is a term because   sqrt(4*4) = sqrt(4) + sqrt(4);

%e   941 is a term because sqrt(9*4*1) = sqrt(9) + sqrt(4) + sqrt(1).

%t Select[Range[10^6], Sqrt[Times @@ #] == Total[Sqrt@ #] &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Feb 02 2017 *)

%o (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

%Y Cf. A007953, A007954, A034710.

%K nonn,base

%O 1,2

%A _José de Jesús Camacho Medina_, Jan 28 2017

%E More terms from _Jon E. Schoenfield_, Jan 30 2017