A343733 - OEIS

%I #6 Jun 02 2021 22:58:34

%S 2,3,7,31,127,8191,131071,524287,2147483647,2305843009213693951,

%T 618970019642690137449562111,162259276829213363391578010288127,

%U 170141183460469231731687303715884105727

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

%C 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).

%e 2^2 has 3 = 3^1 divisors, so 2 is a term.

%e 3^3 has 4 = 2^2 divisors, so 3 is a term.

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

%Y Cf. A000005, A000668, A000312, A062319.

%K nonn,hard

%O 1,1

%A _Jon E. Schoenfield_, Jun 01 2021