A396685 Numbers k such that 2*k is not the range of A002322, the reduced totient function.

7, 13, 17, 19, 25, 31, 34, 37, 38, 43, 47, 49, 57, 59, 61, 62, 67, 71, 73, 76, 77, 79, 85, 91, 93, 94, 97, 101, 103, 107, 109, 118, 121, 122, 124, 127, 129, 133, 137, 139, 142, 143, 149, 151, 152, 157, 161, 163, 167, 169, 170, 175, 177, 181, 185, 187, 188, 193, 197, 199

Offset

1,1

Comments

Numbers k such that 2*k is not in A002174.

For prime p >= 5, p^k is in this sequence if and only if 2*p^k + 1 is composite: if psi(k) = 2*p^k, then k must have some prime power factor q such that psi(q) = 2*q^k. No prime power with exponent >= 2 can satisfy this equation, so q = 2*p^k + 1 must be prime. In particular, this sequence contains p^k with either p == 1 (mod 3) or k even (since then 2*p^k + 1 is divisible by 3).

Links

Jianing Song, Table of n, a(n) for n = 1..10001

Prog

(PARI) isA396685(n) = !is(2*n) \\ See Charles R Greathouse IV's second program in A002174

Crossrefs

Cf. A002322, A079695 (for EulerPhi), A396684 (complement).

Sequence in context: A393401 A079697 A079695 * A079698 A237609 A038906

Adjacent sequences: A396682 A396683 A396684 * A396686 A396687 A396688

Keyword

nonn

Author

Jianing Song, Jun 02 2026

Status

approved