A396553 Numbers k such that EulerPhi(psi(k)) is a power of 2, where psi = A002322 is the reduced totient function.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 26, 28, 30, 31, 32, 33, 34, 35, 36, 39, 40, 41, 42, 44, 45, 48, 50, 51, 52, 55, 56, 60, 61, 62, 63, 64, 65, 66, 68, 70, 72, 75, 77, 78, 80, 82, 84, 85, 88, 90, 91, 93, 96, 97, 99, 100, 102, 103

Offset

1,2

Comments

Numbers k such that psi(k) is in A003401.

Numbers k such that values taken by chi are all constructible numbers for all Dirichlet characters chi modulo k.

Links

Jianing Song, Table of n, a(n) for n = 1..10000

Wikipedia, Constructible number.

Wikipedia, Dirichlet character.

Example

The Dirichlet characters modulo 103 have orders 1, 2, 3, 6, 17, 34, 51, or 102. Since exp(2*Pi*I/d) is always a constructible number when d takes these values (in other words, a regular polygon with 3, 6, 17, 34, 51, or 102 sides can be constructed with compass and straightedge), 103 is a term.

Prog

(PARI) ispower2(n) = (bitand(n, n-1) == 0)
isA396553(n) = ispower2(eulerphi(A002322(n))) \\ see A002322 for its program

Crossrefs

Cf. A002322, A003401, A335120 (prime terms), A396554 (complement).

Sequence in context: A239427 A255422 A080681 * A366186 A272322 A356800

Adjacent sequences: A396550 A396551 A396552 * A396554 A396555 A396556

Keyword

nonn

Author

Jianing Song, May 29 2026

Status

approved