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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). 3

%I

%S 120120,157080,175560,185640,207480,212520,251160,267960,270270,

%T 271320,286440,291720,316680,326040,328440,338520,341880,353430,

%U 367080,378840,394680,395010,397320,404040,408408,414120,417690,426360,434280,442680

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

%H T. D. Noe, <a href="/A190378/b190378.txt">Table of n, a(n) for n = 1..1000</a>

%H Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>

%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>

%e From _Petros Hadjicostas_, Oct 26 2019: (Start)

%e a(1) = (2^3)*3*5*7*11*13 = 120120;

%e a(2) = (2^3)*3*5*7*11*17 = 157080,

%e a(3) = (2^3)*3*5*7*11*19 = 175560;

%e a(4) = (2^3)*3*5*7*13*17 = 185640;

%e a(5) = (2^3)*3*5*7*13*19 = 207480;

%e a(6) = (2^3)*3*5*7*11*23 = 212520;

%e a(7) = (2^3)*3*5*7*13*23 = 251160;

%e a(8) = (2^3)*3*5*7*11*29 = 267960;

%e a(9) = 2*(3^3)*5*7*11*13 = 270270.

%e (End)

%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,1,1,3};Select[Range[1000000],f]

%o (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 Cf. A190110, A190111.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 09 2011

%E Name edited by _Petros Hadjicostas_, Oct 26 2019

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Last modified January 25 06:09 EST 2021. Contains 340416 sequences. (Running on oeis4.)