A065746 Number of divisors of squares of all true powers of primes: a(n) = A000005(A025475(n+1)^2).

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..93.

Formula

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

Example

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

Mathematica

DivisorSigma[0, Select[Range[60000], ! PrimeQ[#] && PrimePowerQ[#] &]^2] (* Amiram Eldar, Apr 13 2024 *)

Crossrefs

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

Sequence in context: A217167 A348052 A195498 * A065478 A109353 A247827

Adjacent sequences: A065743 A065744 A065745 * A065747 A065748 A065749

Keyword

nonn,changed

Author

Labos Elemer, Nov 16 2001

Extensions

Name corrected by Amiram Eldar, Apr 13 2024

Status

approved