This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A065773 #24 Jan 31 2025 04:21:41
%S A065773 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,
%T A065773 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,
%U A065773 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
%N A065773 Number of divisors of square of true prime powers arising in A065405.
%H A065773 Amiram Eldar, <a href="/A065773/b065773.txt">Table of n, a(n) for n = 1..500</a>
%F A065773 a(n) = A000005(A065405(n)^2).
%F A065773 If A065405(n) = q^c, a prime-power, then sigma(q^(2c)) = A000203(q^(2c)) = (-1 + q^(2c+1))/(q-1) = (-1 + q^A000005(A065405(n)^2))/(q-1) also a prime, from A065403.
%e A065773 For k = 3125, tau(k^2) = 11, sigma(k^2) = 12207031 = (5^(tau(k^2)) - 1)/4 = A065403(16) is also a prime.
%t A065773 DivisorSigma[0, Select[Range[10^5], ! PrimeQ[#] && PrimeQ[DivisorSigma[1, #^2]] &]^2] (* _Amiram Eldar_, Jan 31 2025 *)
%o A065773 (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
%Y A065773 Cf. A000005, A065405, A000203, A065403, A065771, A065772, A025475.
%K A065773 nonn
%O A065773 1,1
%A A065773 _Labos Elemer_ and _Robert G. Wilson v_, Nov 19 2001