A263581 Prime powers (p^k, p prime, k >= 1) such that k*p^k - 1 is also a power of a prime.

2, 3, 4, 5, 8, 9, 17, 25, 49, 64, 121, 169, 257, 289, 729, 841, 1681, 1849, 3481, 5329, 11881, 12769, 16129, 18769, 24649, 32041, 32761, 38809, 39601, 44521, 59049, 63001, 65537, 69169, 76729, 85849, 96721, 124609, 134689, 143641, 167281, 175561, 187489

Offset: 1

Author

Juri-Stepan Gerasimov, Apr 09 2016

Keywords

• nonn

Comments

Of course 1 = p^0 for any prime p, so 1 is definitely the power of a prime (comment in A000961).

Only primes of the form 2^m + 1 (2 and Fermat primes) are terms.

Examples

			8 is in this sequence because both 8 = 2^3 and 3*2^3 - 1 = 23 is prime power.
		

Crossrefs

Cf. A000961, A019434 (Fermat primes), A092506 (primes of the form 2^m + 1).

Programs

PARI

ispp(n) = if ((n==1) || isprime(n), return (1), isprimepower(n));
isok(n) = ((k=ispp(n)) && ispp(k*n-1)); \\ Michel Marcus, Apr 11 2016