A066733 Numbers such that the nonzero product of the digits of its square is also a square.

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

1,2

Links

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

Example

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

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 *)

Prog

(PARI) ProdD(x)= { local(p=1); while (x>9 && p>0, p*=x%10; x\=10); return(p*x) } { n=0; for (m=1, 10^10, if (issquare(p=ProdD(m^2)) && p > 0, write("b066733.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Mar 20 2010

Crossrefs

Cf. A067071.

Sequence in context: A080140 A019568 A128458 * A049623 A302506 A228828

Adjacent sequences: A066730 A066731 A066732 * A066734 A066735 A066736

Keyword

nonn,base

Author

Robert G. Wilson v, Jan 15 2002

Status

approved