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A180648
Numbers k such that 1 + phi(k)^4 is a prime. Phi is Euler's totient function.
1
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 18, 25, 29, 32, 33, 34, 35, 39, 40, 44, 45, 47, 48, 50, 52, 56, 58, 60, 65, 66, 70, 72, 78, 81, 83, 84, 87, 89, 90, 94, 104, 105, 107, 112, 115, 116, 123, 130, 140, 144, 156, 161, 162, 164, 165, 166, 168, 174, 176, 178, 180, 181
OFFSET
1,2
COMMENTS
The sequence appears to be infinite, but I have no proof.
LINKS
EXAMPLE
35 is a term since 1 + phi(35)^4 = 1 + 24^4 = 331777 is prime.
MATHEMATICA
Select[Range[200], PrimeQ[1+EulerPhi[#]^4]&] (* Harvey P. Dale, Jul 22 2022 *)
PROG
(Python)
from sympy import isprime, totient
print([n for n in range(1, 10**3) if isprime(1+totient(n)**4)]) # Dumitru Damian, Jan 29 2022
(PARI) isok(k) = isprime(1+eulerphi(k)^4); \\ Michel Marcus, Jan 30 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Carmine Suriano, Sep 14 2010
STATUS
approved