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

1,2

Comments

All the terms are odd squarefree numbers.

Links

Table of n, a(n) for n=1..56.

Mathematica

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

Prog

(Python)
from sympy import totient, isprime
print([k for k in range(1, 340) if isprime(2*totient(k) + k)])
(PARI) isok(k) = isprime(k+2*eulerphi(k)); \\ Michel Marcus, Aug 20 2023

Crossrefs

Cf. A000010, A068080.

Subsequence of A056911.

Subsequence: A088878 (the prime terms).

Sequence in context: A247648 A117203 A081118 * A355918 A003255 A263321

Adjacent sequences: A363580 A363581 A363582 * A363584 A363585 A363586

Keyword

nonn,easy

Author

Darío Clavijo, Aug 17 2023

Status

approved