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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
OFFSET
1,2
LINKS
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) isok(k)={my(p=vecprod(digits(k^4))); p && ispower(p, 4)} \\ Harry J. Smith, Mar 20 2010
CROSSREFS
Cf. A067071.
Sequence in context: A039556 A356729 A095627 * A146337 A165462 A261464
KEYWORD
nonn,base
AUTHOR
Robert G. Wilson v, Jan 15 2002
STATUS
approved