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A066733 Numbers such that the nonzero product of the digits of its square is also a square. 1

%I #12 Jan 03 2016 17:22:19

%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 nonzero product of the digits of its square is also a square.

%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) 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

%Y Cf. A067071.

%K nonn,base

%O 1,2

%A _Robert G. Wilson v_, Jan 15 2002

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Last modified March 28 07:30 EDT 2024. Contains 371235 sequences. (Running on oeis4.)