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

0,3

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A317594 A226752 A043527 * A110401 A213156 A164813

Adjacent sequences: A117717 A117718 A117719 * A117721 A117722 A117723

Keyword

base,nonn

Author

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

Extensions

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

Status

approved