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%I #15 Feb 20 2018 11:35:00
%S 1,118,144,211,427,739,1836,8958,19638,20528,21454,22359,24533,26022,
%T 27378,29648,33038,33204,33648,40226,40262,46416,47181,47198,49314,
%U 53133,55273,55792,59559,59754,60924,61292,61763,61933,66408,68302
%N Numbers such that the nonzero product of the digits of its 4th power is also a 4th power.
%H Harry J. Smith, <a href="/A066734/b066734.txt">Table of n, a(n) for n = 1..1000</a>
%e 118 is in the sequence because the 4th power of 118 is 193877776 and 1*9*3*8*7*7*7*7*6 = 3111696 = 42^4.
%t Do[a = Apply[Times, IntegerDigits[n^2]]; If[ a != 0 && IntegerQ[a^(1/2)], Print[n]], {n, 1, 10^4} ]
%t d4pQ[n_]:=Module[{t=Times@@IntegerDigits[n^4]},t!=0&&IntegerQ[Surd[t,4]]]; Select[Range[70000],d4pQ] (* _Harvey P. Dale_, Feb 20 2018 *)
%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 ((p=ProdD(m^4)) == 0 || (s=sqrt(p)) % 1 , next); if (sqrt(s)%1 == 0, write("b066734.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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