A066733 Numbers such that the product of the digits of its square is a square > 0.

1, 2, 3, 7, 12, 17, 21, 38, 88, 106, 107, 108, 109, 117, 122, 128, 129, 141, 146, 164, 168, 171, 173, 178, 191, 196, 204, 206, 207, 208, 209, 212, 221, 222, 236, 263, 276, 278, 288, 306, 342, 359, 364, 367, 372, 377, 394, 432, 463, 478, 479, 518, 537, 538

Offset: 1

Author

Robert G. Wilson v, Jan 15 2002

Keywords

• nonn
• base

Examples

			17 is in the sequence because the square of 17 is 289 and 2*8*9 = 144 = 12^2.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067071.

Programs

Mathematica

Do[a = Apply[Times, IntegerDigits[n^2]]; If[ a != 0 && IntegerQ[a^(1/2)], Print[n]], {n, 1, 10^4} ]
nzpQ[n_]:=Module[{prod=Times@@IntegerDigits[n^2]},prod!=0 && IntegerQ[ Sqrt[ prod]]]; Select[Range[600],nzpQ] (* Harvey P. Dale, May 27 2012 *)

PARI

isok(k)= { my(p=vecprod(digits(k^2))); p > 0 && issquare(p) } \\ Harry J. Smith, Mar 20 2010