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%I #18 Mar 07 2024 01:30:06
%S 5400,9000,10584,13500,24696,26136,36504,37044,49000,62424,68600,
%T 77976,95832,114264,121000,143748,158184,165375,169000,171500,181656,
%U 207576,231525,237276,266200,289000,295704,332024,353736,361000,363096
%N Numbers with prime factorization p^2*q^3*r^3 where p, q, and r are distinct primes.
%H T. D. Noe, <a href="/A190106/b190106.txt">Table of n, a(n) for n = 1..1000</a>
%H Will Nicholes, <a href="https://willnicholes.com/2010/06/06/list-of-prime-signatures">List of prime signatures</a>, 2010.
%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(3)^2/2 - P(2)*P(6)/2 - P(3)*P(5) + P(8) = 0.00085907862422456410530..., where P is the prime zeta function. - _Amiram Eldar_, Mar 07 2024
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,3,3};Select[Range[500000],f]
%o (PARI) list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\4)^(1/6), t1=p^3;forprime(q=p+1, (lim\t1)^(1/3), t2=t1*q^3;forprime(r=2, sqrt(lim\t2), if(p==r||q==r, next);listput(v,t2*r^2)))); vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 20 2011
%Y Cf. A179691, A179698, A179746, A189991.
%Y Cf. A085548, A085541, A085965, A085966, A085968.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 04 2011
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