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A178212 Nonsquarefree numbers divisible by exactly three distinct primes.

%I A178212 #36 Nov 05 2024 12:03:50
%S A178212 60,84,90,120,126,132,140,150,156,168,180,198,204,220,228,234,240,252,
%T A178212 260,264,270,276,280,294,300,306,308,312,315,336,340,342,348,350,360,
%U A178212 364,372,378,380,396,408,414,440,444,450,456,460,468,476,480,490,492
%N A178212 Nonsquarefree numbers divisible by exactly three distinct primes.
%H A178212 Reinhard Zumkeller, <a href="/A178212/b178212.txt">Table of n, a(n) for n = 1..10000</a>
%F A178212 A001221(a(n)) = 3; A001222(a(n)) > 3; A000005(n) >= 12;
%F A178212 a(n) = A123712(n) for n <= 52, possibly more.
%e A178212 60 is in the sequence because it is not squarefree and it is divisible by three distinct primes: 2, 3, 5.
%e A178212 72 is not in the sequence, because although it is not squarefree, it is divisible by only two distinct primes: 2 and 3.
%t A178212 nsD3Q[n_] := Block[{fi = FactorInteger@ n}, Length@ fi == 3 && Plus @@ Last /@ fi > 3]; Select[ Range@ 494, nsD3Q] (* _Robert G. Wilson v_, Feb 09 2012 *)
%t A178212 Select[Range[500], PrimeNu[#] == 3 && PrimeOmega[#] > 3 &] (* _Alonso del Arte_, Mar 23 2015, based on a comment from _Robert G. Wilson v_, Feb 09 2012; requires Mathematica 7.0+ *)
%o A178212 (PARI) is_A178212(n)={ omega(n)==3 & bigomega(n)>3 }
%o A178212 for(n=1,999,is_A178212(n) & print1(n",")) \\ _M. F. Hasler_, Feb 09 2012
%o A178212 (Haskell)
%o A178212 a178212 n = a178212_list !! (n-1)
%o A178212 a178212_list = filter f [1..] where
%o A178212    f x = length (a027748_row x) == 3 && any (> 1) (a124010_row x)
%o A178212 -- _Reinhard Zumkeller_, Apr 03 2015
%Y A178212 A subsequence of A033987.
%Y A178212 A085987 is a subsequence.
%Y A178212 Cf. A007304, A200511, A200521.
%Y A178212 Cf. A000005, A001221, A001222, A013929, A085987, A123712.
%Y A178212 Cf. A027748, A124010.
%Y A178212 Subsequence of A375055, which differs starting at a(43) = 440 > A375055(43) = 420.
%K A178212 nonn
%O A178212 1,1
%A A178212 _Reinhard Zumkeller_, May 24 2010