

A066734


Numbers such that the nonzero product of the digits of its 4th power is also a 4th power.


1



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

1,2


LINKS

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


EXAMPLE

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.


MATHEMATICA

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 *)


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 ((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


CROSSREFS

Cf. A067071.
Sequence in context: A066923 A039556 A095627 * A146337 A165462 A261464
Adjacent sequences: A066731 A066732 A066733 * A066735 A066736 A066737


KEYWORD

nonn,base


AUTHOR

Robert G. Wilson v, Jan 15 2002


STATUS

approved



