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A065746
Number of divisors of squares of all true powers of primes: a(n) = A000005(A025475(n+1)^2).
0
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
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 16 2001
EXTENSIONS
Name corrected by Amiram Eldar, Apr 13 2024
STATUS
approved