This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A190470 #15 Mar 07 2024 01:27:28
%S A190470 21600,36000,42336,48600,95256,98784,104544,121500,146016,196000,
%T A190470 225000,235224,249696,274400,311904,328536,333396,337500,383328,
%U A190470 457056,484000,561816,632736,676000,701784,726624,830304,1028376,1064800,1156000
%N A190470 Numbers with prime factorization p^2*q^3*r^5 where p, q, and r are distinct primes.
%H A190470 T. D. Noe, <a href="/A190470/b190470.txt">Table of n, a(n) for n = 1..1000</a>
%H A190470 Will Nicholes, <a href="https://willnicholes.com/2010/06/06/list-of-prime-signatures">List of prime signatures</a>, 2010.
%H A190470 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>.
%F A190470 Sum_{n>=1} 1/a(n) = P(2)*P(3)*P(5) - P(2)*P(8) - P(3)*P(7) - P(5)^2 + 2*P(10) = 0.00025025315357155375895..., where P is the prime zeta function. - _Amiram Eldar_, Mar 07 2024
%t A190470 f[n_]:=Sort[Last/@FactorInteger[n]]=={2,3,5}; Select[Range[2500000],f] (*and*) lst={}; Do[If[k!=n && k!=m && n!=m, AppendTo[lst, Prime[k]^2*Prime[n]^3*Prime[m]^5]], {n,20}, {m,20}, {k,20}]; Take[Union@lst,60]
%o A190470 (PARI) list(lim)=my(v=List(),t1,t2);forprime(p=2, (lim\72)^(1/5), t1=p^5;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 A190470 Cf. A190467, A190468, A190469.
%Y A190470 Cf. A085548, A085541, A085965, A085967, A085968.
%K A190470 nonn
%O A190470 1,1
%A A190470 _Vladimir Joseph Stephan Orlovsky_, May 10 2011