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%I #8 May 13 2013 01:49:24
%S 120,168,180,252,264,270,280,300,312,378,396,408,440,450,456,468,520,
%T 552,588,594,612,616,680,684,696,700,702,728,744,750,760,828,882,888,
%U 918,920,945,952,980,984,1026,1032,1044,1064,1100,1116,1128,1144,1160
%N Product of exactly 5 primes, 3 of which are distinct.
%H T. D. Noe, <a href="/A179642/b179642.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>
%e 120=2^3*3*5, 168=2^3*3*7, 180=2^2*3^2*5, 252=2^2*3^2*7, 264=2^3*3*11, 270=2*3^3*5
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,3} || Sort[Last/@FactorInteger[n]]=={1,2,2}; Select[Range[2000], f]
%o (PARI) list(lim)=my(v=List(),t);forprime(p=2,(lim\6)^(1/3),forprime(q=2,sqrt(lim\p^3),if(p==q,next);t=p^3*q;forprime(r=q+1,lim\t,if(p==r,next);listput(v,t*r))));forprime(p=2,sqrt(lim\12),forprime(q=p+1,sqrt(lim\p^2\2),t=(p*q)^2;forprime(r=2,lim\t,if(p==r||q==r,next);listput(v,t*r))));vecsort(Vec(v)) \\ _Charles R Greathouse IV_, Jul 19 2011
%Y Union of A189975 and A179643.
%Y Cf. A006881, A007304, A085986, A085987, A178739.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 21 2010
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