A048184 Primes with nontrivial omnipower group.

3, 5, 7, 11, 17, 19, 23, 47, 59, 83, 107, 163, 167, 179, 227, 251, 257, 263, 347, 359, 383, 467, 479, 487, 503, 563, 587, 719, 839, 863, 887, 983, 1019, 1187, 1283, 1307, 1319, 1367, 1439, 1459, 1487, 1523, 1619, 1823, 1907, 2027, 2039, 2063, 2099, 2207

Offset

1,1

Comments

k is an omnipower of odd prime p if k is an n-th power (mod p) for all 1 <= n < (p-1)/2.

Nonzero omnipowers of p form a subgroup of the multiplicative group mod p.

Primes of form 2p^k+1, p prime, k >= 0. That is, primes p such that (p-1)/2 is a prime power (A000961).

Links

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

Formula

a(n) = 2*A364926(n) + 1. - Amiram Eldar, Mar 18 2026

Mathematica

q[k_] := k > 2 && PrimeQ[k] && ((k-1)/2 == 1 || PrimePowerQ[(k-1)/2]); Select[Range[2300], q] (* Amiram Eldar, Mar 18 2026 *)

Prog

(PARI) isA048184(n) = (n==3) || (isprime(n) && (n>2) && isprimepower((n-1)/2))

Crossrefs

Supersequence of A005385.

Cf. A000961, A364926.

Sequence in context: A139559 A158361 A342692 * A290283 A163420 A155489

Adjacent sequences: A048181 A048182 A048183 * A048185 A048186 A048187

Keyword

nonn,easy

Author

David W. Wilson

Status

approved