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A066734
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Numbers such that the nonzero product of the digits of its 4th power is also a 4th power.
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1
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1, 118, 144, 211, 427, 739, 1836, 8958, 19638, 20528, 21454, 22359, 24533, 26022, 27378, 29648, 33038, 33204, 33648, 40226, 40262, 46416, 47181, 47198, 49314, 53133, 55273, 55792, 59559, 59754, 60924, 61292, 61763, 61933, 66408, 68302
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Do[a = Apply[Times, IntegerDigits[n^2]]; If[ a != 0 && IntegerQ[a^(1/2)], Print[n]], {n, 1, 10^4} ]
d4pQ[n_]:=Module[{t=Times@@IntegerDigits[n^4]}, t!=0&&IntegerQ[Surd[t, 4]]]; Select[Range[70000], d4pQ] (* Harvey P. Dale, Feb 20 2018 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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