OFFSET
1,2
COMMENTS
Corresponding values of phi include 1, 16, 256, 1296, 4096, ... and these arise several times each.
a(3) = A053576(4).
A013776 is a subsequence since phi(2^(4*n+1)) = (2^n)^4. - Bernard Schott, Sep 22 2022
Subsequence of primes is A037896 since in this case: phi(k^4+1) = k^4. - Bernard Schott, Mar 05 2023
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
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 *)
PROG
(PARI) is(n)=ispower(eulerphi(n), 4) \\ Charles R Greathouse IV, Apr 24 2020
(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)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 27 2002
STATUS
approved