A363583 Numbers k such that 2*phi(k)+k is a prime, where phi is A000010.

1, 3, 5, 7, 11, 13, 15, 23, 33, 35, 37, 43, 47, 53, 61, 67, 69, 71, 77, 87, 95, 103, 113, 119, 123, 127, 133, 137, 143, 159, 163, 167, 177, 181, 191, 193, 209, 211, 217, 249, 251, 257, 259, 263, 267, 271, 277, 293, 299, 307, 313, 329, 331, 335, 337, 339

Offset: 1

Author

Darío Clavijo, Aug 17 2023

Keywords

• nonn
• easy

Comments

All the terms are odd squarefree numbers.

Crossrefs

Cf. A000010, A068080.

Subsequence of A056911.

Subsequence: A088878 (the prime terms).

Programs

Mathematica

Select[Range[1, 350, 2], PrimeQ[2*EulerPhi[#] + #] &] (* Amiram Eldar, Aug 17 2023 *)

PARI

isok(k) = isprime(k+2*eulerphi(k)); \\ Michel Marcus, Aug 20 2023

Python

from sympy import totient, isprime
print([k for k in range(1, 340) if isprime(2*totient(k) + k)])