A180648 Numbers k such that 1 + phi(k)^4 is a prime. Phi is Euler's totient function.

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

Dumitru Damian, Table of n, a(n) for n = 1..10000

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

Cf. A000010, A000040, A002808, A018252.

Sequence in context: A355596 A246077 A064915 * A322605 A175740 A320321

Adjacent sequences: A180645 A180646 A180647 * A180649 A180650 A180651

Keyword

nonn

Author

Carmine Suriano, Sep 14 2010

Status

approved