%I A065773
%S A065773 5,7,7,5,13,7,5,17,5,19,5,13,5,5,7,11,7,5,5,5,13,5,7,31,5,5,5,5,5,5,13,
%T A065773 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,
%U A065773 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.
%F A065773 a(n)=A000005[A065405(n)^2], 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 n = 3125, tau[nn] = 11, sigma[nn] = 12207031 = (5^(tau[nn])-1)/4 = A065403[16] 
               is also a prime.
%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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Oct 30 2009]
%Y A065773 Cf. A000005, A065405, A000203, A065771, A065772, A025475.
%Y A065773 DivisorSigma[0, (A065405)^2].
%Y A065773 Sequence in context: A020760 A011269 A093723 this_sequence A114916 A001989 
               A086056
%Y A065773 Adjacent sequences: A065770 A065771 A065772 this_sequence A065774 A065775 
               A065776
%K A065773 nonn
%O A065773 1,1
%A A065773 Labos E. (labos(AT)ana.sote.hu) and Robert G. Wilson v (rgwv(AT)rgwv.com), 
               Nov 19 2001