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%I #17 Mar 07 2024 01:29:41
%S 10800,16200,18000,21168,31752,40500,45000,49392,52272,67500,73008,
%T 78408,98000,109512,111132,124848,137200,155952,172872,187272,191664,
%U 228528,233928,242000,245000,259308,316368,338000,342792,363312,415152
%N Numbers with prime factorization p^2*q^3*r^4 where p, q, and r are distinct primes.
%H T. D. Noe, <a href="/A190115/b190115.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)*P(4) - P(2)*P(7) - P(3)*P(6) - P(4)*P(5) + 2*P(9) = 0.00061171477910848082277..., where P is the prime zeta function. - _Amiram Eldar_, Mar 07 2024
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,3,4};Select[Range[900000],f]
%o (PARI) list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\72)^(1/4), t1=p^4;forprime(q=2, (lim\t1)^(1/3), if(p==q, next);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 24 2011
%Y Cf. A093770, A190012, A190014.
%Y Cf. A085548, A085541, A085964, A085965, A085966, A085967, A085969.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 04 2011
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