%I #22 Jul 06 2020 02:38:35
%S 288,800,972,1568,3872,5408,6075,9248,11552,11907,12500,16928,26912,
%T 28125,29403,30752,41067,43808,53792,59168,67228,70227,70688,87723,
%U 89888,111392,119072,128547,143648,151263,153125,161312,170528,199712
%N Product of the 5th power of a prime and different distinct prime of the 2nd power (p^5*q^2).
%C 288=2^5*3^2, 800=2^5*5^2,..
%H T. D. Noe, <a href="/A179646/b179646.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>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%F Sum_{n>=1} 1/a(n) = P(2)*P(5) - P(7) = A085548 * A085965 - A085967 = 0.007886..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,5}; Select[Range[200000], f]
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2,(lim\4)^(1/5),t=p^5;forprime(q=2,sqrt(lim\t),if(p==q,next);listput(v,t*q^2)));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011
%Y Cf. A030636, A046308, A007774.
%Y Cf. A085548, A085965, A085967.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 21 2010