%I #15 Jul 06 2020 02:42:05
%S 7776,100000,537824,759375,4084101,5153632,11881376,39135393,45435424,
%T 52521875,79235168,90224199,205962976,345025251,503284375,601692057,
%U 656356768,916132832,1160290625,1564031349,2219006624,2706784157,3707398432
%N Numbers with prime factorization p^5q^5.
%H T. D. Noe, <a href="/A190465/b190465.txt">Table of n, a(n) for n = 1..1000</a>
%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%F Sum_{n>=1} 1/a(n) = (P(5)^2 - P(10))/2 = (A085965^2 - P(10))/2 = 0.000142..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1}; Select[Range[10000],f]^5
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2, lim^(1/10), t=p^5;forprime(q=p+1, (lim\t)^(1/5), listput(v,t*q^5))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011
%Y Cf. A179699, A179705, A190464.
%Y Cf. A085965.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 10 2011