A117720 Numbers for which the sum of the digits is the square root of the product of their digits.

0, 1, 999, 2558, 2585, 2855, 3366, 3636, 3663, 4444, 5258, 5285, 5528, 5582, 5825, 5852, 6336, 6363, 6633, 8255, 8525, 8552, 12489, 12498, 12849, 12894, 12948, 12984, 13377, 13737, 13773, 14289, 14298, 14829, 14892, 14928, 14982, 17337, 17373

Offset: 0

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 13 2006

Keywords

• base
• nonn

Examples

			2558 is in the sequence because (1)the sum of its digits is 2+5+5+8=20,(2)the product of its digits is 2*5*5*8=400 and 20 is the square root of 400.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Programs

Mathematica

sdsqrQ[n_]:=Module[{idn=IntegerDigits[n]},Total[idn]==Sqrt[Times@@idn]]; Select[Range[0,18000],sdsqrQ] (* Harvey P. Dale, Oct 20 2012 *)

PARI

sudig(i,suOrmul)= { local(nshft,resul) ; nshft = i ; resul = nshft % 10 ; nshft = nshft \ 10 ; while(nshft>0, if(suOrmul==0, resul += nshft % 10, resul *= nshft % 10 ) ; nshft \= 10 ; ) ; return(resul) ; }
{ for(n=0,15000, summ = sudig(n,0) ; mull = sudig(n,1) ; if( summ^2==mull, print1(n,",") ) ; ) ; } \\ R. J. Mathar, Apr 21 2006

Extensions

More terms from R. J. Mathar, Apr 21 2006