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%I #9 Jan 31 2017 16:46:06
%S 16,24,36,60,81,84,100,126,132,140,150,156,196,204,220,228,234,260,
%T 276,308,315,330,340,342,348,364,372,375,380,444,460,476,484,490,492,
%U 495,510,516,525,532,558,564,572,580,585,620,625,636,644,650,666,676,690
%N 4-almost primes p * q * r * s not relatively prime to p + q + r + s.
%C p, q, r, s are not necessarily distinct. The converse to this is A110227: 4-almost primes p * q * r * s which are relatively prime to p+q+r+s.
%H Charles R Greathouse IV, <a href="/A110228/b110228.txt">Table of n, a(n) for n = 1..10000</a>
%e 84 is in this sequence because 84 = 2^2 * 3 * 7 and the sum of these prime factors is 2 + 2 + 3 + 7 = 14 = 2 * 7, which is a divisor of 84.
%o (PARI) list(lim)=my(v=List()); forprime(p=2,lim\8, forprime(q=2,min(p,lim\4\p), my(pq=p*q); forprime(r=2,min(lim\pq\2,q), my(pqr=pq*r,t); forprime(s=2,min(lim\pqr,r), t=pqr*s; if(gcd(t,p+q+r+s)>1, listput(v,t)))))); Set(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y Cf. A014613, A110187, A110188, A110227, A110229, A110230, A110231, A110232, A110289, A110290, A110296, A110297.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jul 16 2005
%E Corrected and extended by _Ray Chandler_, Jul 20 2005
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