A065773 Number of divisors of square of true prime powers arising in A065405.
5, 7, 7, 5, 13, 7, 5, 17, 5, 19, 5, 13, 5, 5, 7, 11, 7, 5, 5, 5, 13, 5, 7, 31, 5, 5, 5, 5, 5, 5, 13, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 7, 7, 5, 5, 5, 5, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5
Offset: 1
Keywords
Examples
For k = 3125, tau(k^2) = 11, sigma(k^2) = 12207031 = (5^(tau(k^2)) - 1)/4 = A065403(16) is also a prime.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..500
Programs
-
Mathematica
DivisorSigma[0, Select[Range[10^5], ! PrimeQ[#] && PrimeQ[DivisorSigma[1, #^2]] &]^2] (* Amiram Eldar, Jan 31 2025 *)
-
PARI
{ n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), a=numdiv(m^2); write("b065773.txt", n++, " ", a); if (n==100, return)) ) } \\ Harry J. Smith, Oct 30 2009