A066734 Numbers such that the nonzero product of the digits of its 4th power is also a 4th power.

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

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: A039556 A356729 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