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A190378 Numbers with prime factorization p*q*r*s*t*u^3 (where p, q, r, s, t, u are distinct primes).

%I A190378 #21 Oct 26 2019 02:28:22
%S A190378 120120,157080,175560,185640,207480,212520,251160,267960,270270,
%T A190378 271320,286440,291720,316680,326040,328440,338520,341880,353430,
%U A190378 367080,378840,394680,395010,397320,404040,408408,414120,417690,426360,434280,442680
%N A190378 Numbers with prime factorization p*q*r*s*t*u^3 (where p, q, r, s, t, u are distinct primes).
%H A190378 T. D. Noe, <a href="/A190378/b190378.txt">Table of n, a(n) for n = 1..1000</a>
%H A190378 Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>
%H A190378 <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%e A190378 From _Petros Hadjicostas_, Oct 26 2019: (Start)
%e A190378 a(1) = (2^3)*3*5*7*11*13 = 120120;
%e A190378 a(2) = (2^3)*3*5*7*11*17 = 157080,
%e A190378 a(3) = (2^3)*3*5*7*11*19 = 175560;
%e A190378 a(4) = (2^3)*3*5*7*13*17 = 185640;
%e A190378 a(5) = (2^3)*3*5*7*13*19 = 207480;
%e A190378 a(6) = (2^3)*3*5*7*11*23 = 212520;
%e A190378 a(7) = (2^3)*3*5*7*13*23 = 251160;
%e A190378 a(8) = (2^3)*3*5*7*11*29 = 267960;
%e A190378 a(9) = 2*(3^3)*5*7*11*13 = 270270.
%e A190378 (End)
%t A190378 f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,1,1,3};Select[Range[1000000],f]
%o A190378 (PARI) list(lim)=my(v=List(),t1,t2,t3,t4,t5); forprime(p=2,sqrtnint(lim\2310, 3), t1=p^3; forprime(q=2,lim\(210*t1), if(q==p, next); t2=q*t1; forprime(r=2,lim\(30*t2), if(r==p || r==q, next); t3=r*t2; forprime(s=2,lim\(6*t3), if(s==p || s==q || s==r, next); t4=s*t3; forprime(t=2,lim\(2*t4), if(t==p || t==q || t==r || t==s, next); t5=t*t4; forprime(u=2,lim\t5, if(u==p || u==q || u==r || u==s || u==t, next); listput(v, t5*u))))))); Set(v) \\ _Charles R Greathouse IV_, Aug 25 2016
%Y A190378 Cf. A190110, A190111.
%K A190378 nonn
%O A190378 1,1
%A A190378 _Vladimir Joseph Stephan Orlovsky_, May 09 2011
%E A190378 Name edited by _Petros Hadjicostas_, Oct 26 2019