A048184 - OEIS

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

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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

PROG

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

CROSSREFS