%I #8 Apr 13 2024 05:15:57

%S 5,7,5,9,5,7,11,5,13,9,5,7,15,5,11,17,5,7,5,19,5,9,13,5,5,21,7,5,5,5,

%T 23,15,7,5,9,5,11,5,5,25,5,7,5,5,5,17,7,5,5,27,5,5,5,5,5,7,5,9,13,5,

%U 29,11,5,5,5,19,5,5,7,5,5,5,9,7,5,5,5,31,5,5,5,5,5,5,7,5,5,5,5,5,21,5,33

%N Number of divisors of squares of all true powers of primes: a(n) = A000005(A025475(n+1)^2).

%F tau(p^(2c)), where tau is the number of divisors, c > 1 and p is prime.

%e tau(p^(2c)) = 2c+1 is prime if c = (odd prime -1)/2 = 1, 2, 3, 5, 6, 8, ... = A005097.

%t DivisorSigma[0, Select[Range[60000], ! PrimeQ[#] && PrimePowerQ[#] &]^2] (* _Amiram Eldar_, Apr 13 2024 *)

%Y Cf. A000005, A025475, A065403, A065404, A065405, A005097.

%K nonn

%O 1,1

%A _Labos Elemer_, Nov 16 2001

%E Name corrected by _Amiram Eldar_, Apr 13 2024