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

Author

Robert G. Wilson v, Jan 15 2002

Keywords

• nonn
• base

Examples

			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.
		

Links

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

Crossrefs

Cf. A067071.

Programs

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 *)

PARI

isok(k)={my(p=vecprod(digits(k^4))); p && ispower(p, 4)} \\ Harry J. Smith, Mar 20 2010