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%I #11 May 15 2019 17:33:02
%S 12,20,28,44,45,52,63,68,75,76,92,99,116,117,124,147,148,153,164,165,
%T 171,172,175,188,207,212,236,244,245,261,268,273,275,279,284,292,316,
%U 325,332,333,345,356,363,369,385,387,388,399,404,412,423,425,428,435
%N 3-almost primes p * q * r relatively prime to p+q+r.
%C A110188 is the converse, 3-almost primes p * q * r not relatively prime to p+q+r.
%H Charles R Greathouse IV, <a href="/A110187/b110187.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 12 because 12 = 2^2 * 3, which is relatively prime to 2 + 2 + 3 = 7.
%e 30 is not in the sequence, since 30 = 2 * 3 * 5, which is in fact divisible by 2 + 3 + 5 = 10.
%e 92 is in the sequence since 92 = 2^2 x 23, 2 + 2 + 23 = 27 = 3^3, (92, 27) = 1.
%t Select[Range[500],PrimeOmega[#]==3&&CoprimeQ[#,Total[Times @@@ FactorInteger[ #]]]&] (* _Harvey P. Dale_, May 15 2019 *)
%o (PARI) list(lim)=my(v=List()); forprime(p=2,lim\4, forprime(q=2,min(p,lim\2\p), my(pq=p*q,t); forprime(r=2,min(lim\pq,q), t=r*pq; if(gcd(t,p+q+r)==1, listput(v,t))))); Set(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y Cf. A014612, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110296, A110297.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jul 15 2005
%E Extended by _Ray Chandler_, Jul 20 2005
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