A396555 - OEIS

A396555

Primes p such that EulerPhi(p-1) is not a power of 2.

19, 23, 29, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 89, 101, 107, 109, 113, 127, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 197, 199, 211, 223, 227, 229, 233, 239, 251, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes p such that the range of chi contains non-constructible numbers for some Dirichlet characters chi modulo p. General k satisfying this condition are listed in A396554.

Primes p such that p-1 is in A003401.

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Constructible number.

Wikipedia, Dirichlet character.

EXAMPLE

19 is a term since there are Dirichlet characters of order 9 or 18 modulo 19, and exp(2*Pi*I/9) and exp(2*Pi*I/18) are not constructible numbers (in other words, a regular polygon with 9 or 18 sides cannot be constructed with compass and straightedge).

23 is a term since there are Dirichlet characters of order 11 or 22 modulo 23, and exp(2*Pi*I/11) and exp(2*Pi*I/22) are not constructible numbers. Note however that these two numbers are constructible using a neusis.

47 is a term since there are Dirichlet characters of order 23 or 46 modulo 47, and exp(2*Pi*I/23) and exp(2*Pi*I/46) are not constructible numbers, even with neusis construction.

MATHEMATICA

Select[Prime[Range[100]], BitAnd[#, # - 1] > 0 & [EulerPhi[# - 1]] &] (* Paolo Xausa, Aug 18 2026 *)

PROG

(PARI) ispower2(n) = (bitand(n, n-1) == 0)

isA396555(p) = (isprime(p) && !ispower2(eulerphi(p-1)))

CROSSREFS

Cf. A000010, A003401, A335120 (complement in primes), A396554.

Sequence in context: A274048 A334093 A120640 * A309360 A151768 A270083

Adjacent sequences: A396552 A396553 A396554 * A396556 A396557 A396558

KEYWORD

nonn

AUTHOR

Jianing Song, May 29 2026

STATUS

approved