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%I #9 Feb 01 2017 09:09:15
%S 256,576,896,960,1296,1344,1440,1600,1944,2112,2160,2240,2496,2916,
%T 3024,3136,3168,3264,3360,3520,3600,3648,4000,4160,4416,4704,4752,
%U 4860,4896,4928,5040,5400,5440,5568,5616,5824,5952,6000,6080,6561,6624,6804,7056
%N 8-almost primes p*q*r*s*t*u*v*w not relatively prime to p+q+r+s+t+u+v+w.
%C The primes p, q, r, s, t, u, v, w are not necessarily distinct. The 8-almost primes are A046310. The converse, A110296, is 8-almost primes p*q*r*s*t*u*v*w which are relatively prime to p+q+r+s+t+u+v+w.
%H Charles R Greathouse IV, <a href="/A110297/b110297.txt">Table of n, a(n) for n = 1..10000</a>
%e 576 = 2^6 * 3^2 is an element of this sequence because its sum of prime factors is 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 = 18 = 2 * 3^2 which is a factor of 576 and not relatively prime to 576.
%o (PARI) list(lim)=my(v=List()); forprime(p=2, lim\128, forprime(q=2, min(p, lim\64\p), my(pq=p*q); forprime(r=2, min(lim\pq\32, q), my(pqr=pq*r); forprime(s=2, min(lim\pqr\16, r), my(pqrs=pqr*s); forprime(t=2, min(lim\pqrs\8, s), my(pqrst=pqrs*t); forprime(u=2, min(lim\pqrst\4, t), my(pqrstu=pqrst*u); forprime(w=2,min(lim\pqrstu\2,u), my(pqrstuw=pqrstu*w,n); forprime(x=2,min(lim\pqrstuw,w), n=pqrstuw*x; if(gcd(n, p+q+r+s+t+u+w+x)>1, listput(v, n)))))))))); Set(v) \\ _Charles R Greathouse IV_, Feb 01 2017
%Y Cf. A046310, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110296.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jul 18 2005
%E Extended by _Ray Chandler_, Jul 20 2005
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