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%I A190111 #15 Oct 26 2019 16:11:39
%S A190111 27720,32760,41580,42840,46200,47880,49140,51480,54600,57960,64260,
%T A190111 64680,67320,71400,71820,72072,73080,75240,76440,77220,78120,79560,
%U A190111 79800,85800,86940,88920,91080,93240,94248,96600,99960,100980,101640,103320
%N A190111 Numbers with prime factorization p*q*r*s^2*t^3 (where p, q, r, s, t are distinct primes).
%H A190111 T. D. Noe, <a href="/A190111/b190111.txt">Table of n, a(n) for n = 1..1000</a>
%H A190111 Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%H A190111 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%e A190111 From _Petros Hadjicostas_, Oct 26 2019: (Start)
%e A190111 a(1) = (2^3)*(3^2)*5*7*11 = 27720;
%e A190111 a(2) = (2^3)*(3^2)*5*7*13 = 32760;
%e A190111 a(3) = (2^2)*(3^3)*5*7*11 = 41580;
%e A190111 a(4) = (2^3)*(3^2)*5*7*17 = 42840;
%e A190111 a(5) = (2^3)*3*(5^2)*7*11 = 46200.
%e A190111 (End)
%t A190111 f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,2,3};Select[Range[150000],f]
%o A190111 (PARI) list(lim)=my(v=List(),t1,t2,t3,t4); forprime(p=2,sqrtnint(lim\420, 3), t1=p^3; forprime(q=2,sqrtint(lim\(30*t1)), if(q==p, next); t2=q^2*t1; forprime(r=2,lim\(6*t2), if(r==p || r==q, next); t3=r*t2; forprime(s=2,lim\(2*t3), if(s==p || s==q || s==r, next); t4=s*t3; forprime(t=2,lim\t4, if(t==p || t==q || t==r || t==s, next); listput(v, t4*t)))))); Set(v) \\ _Charles R Greathouse IV_, Aug 25 2016
%Y A190111 Cf. A179645, A189990, A190109, A190110.
%K A190111 nonn
%O A190111 1,1
%A A190111 _Vladimir Joseph Stephan Orlovsky_, May 04 2011

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