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A078164
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Numbers k such that phi(k) is a perfect biquadrate.
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18
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1, 2, 17, 32, 34, 40, 48, 60, 257, 512, 514, 544, 640, 680, 768, 816, 960, 1020, 1297, 1387, 1417, 1729, 1971, 2109, 2223, 2289, 2331, 2445, 2457, 2565, 2594, 2608, 2774, 2812, 2834, 2835, 3052, 3260, 3458, 3888, 3912, 3924, 3942, 3996, 4104, 4212, 4218
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OFFSET
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1,2
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COMMENTS
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Corresponding values of phi include 1, 16, 256, 1296, 4096, ... and these arise several times each.
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LINKS
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MATHEMATICA
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k=4; Do[s=EulerPhi[n]^(1/k); If[IntegerQ[s], Print[n]], {n, 1, 5000}]
Select[Range[5000], IntegerQ[Surd[EulerPhi[#], 4]]&] (* Harvey P. Dale, Apr 30 2015 *)
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PROG
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(Python)
from itertools import count, islice
from sympy import totient, integer_nthroot
def A078164_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:integer_nthroot(totient(n), 4)[1], count(max(1, startvalue)))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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