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%I #15 Dec 06 2024 20:19:13
%S 1,2,3,7,12,17,21,38,88,106,107,108,109,117,122,128,129,141,146,164,
%T 168,171,173,178,191,196,204,206,207,208,209,212,221,222,236,263,276,
%U 278,288,306,342,359,364,367,372,377,394,432,463,478,479,518,537,538
%N Numbers such that the product of the digits of its square is a square > 0.
%H Harry J. Smith, <a href="/A066733/b066733.txt">Table of n, a(n) for n = 1..1000</a>
%e 17 is in the sequence because the square of 17 is 289 and 2*8*9 = 144 = 12^2.
%t Do[a = Apply[Times, IntegerDigits[n^2]]; If[ a != 0 && IntegerQ[a^(1/2)], Print[n]], {n, 1, 10^4} ]
%t nzpQ[n_]:=Module[{prod=Times@@IntegerDigits[n^2]},prod!=0 && IntegerQ[ Sqrt[ prod]]]; Select[Range[600],nzpQ] (* _Harvey P. Dale_, May 27 2012 *)
%o (PARI) isok(k)= { my(p=vecprod(digits(k^2))); p > 0 && issquare(p) } \\ _Harry J. Smith_, Mar 20 2010
%Y Cf. A067071.
%K nonn,base,changed
%O 1,2
%A _Robert G. Wilson v_, Jan 15 2002