A343733 Primes p at which tau(p^p) is a prime power, where tau is the number-of-divisors function A000005.

2, 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727

Offset: 1

Author

Jon E. Schoenfield, Jun 01 2021

Keywords

• nonn
• hard

Comments

For every prime p, p^p has p+1 divisors. p=2 is a term, but for all odd primes, p+1 is even, so this sequence consists of 2 and the primes of the form 2^j - 1, i.e., 2 and the Mersenne primes (A000668).

Examples

			2^2 has 3 = 3^1 divisors, so 2 is a term.
3^3 has 4 = 2^2 divisors, so 3 is a term.
5^5 has 6 = 2*3 divisors, so 5 is not a term.
		

Crossrefs

Cf. A000005, A000668, A000312, A062319.