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%I #8 Jan 31 2017 16:55:59
%S 64,144,160,216,240,324,336,400,528,540,560,624,729,756,784,816,840,
%T 880,900,912,1040,1104,1134,1188,1215,1232,1260,1320,1350,1360,1392,
%U 1404,1456,1488,1500,1520,1560,1764,1776,1836,1840,1848,1904,1936,1960,1968
%N 6-almost primes p * q * r * s * t * u not relatively prime to p+q+r+s+t+u.
%C p, q, r, s, t, u are not necessarily distinct. The converse to this is A110231: 6-almost primes p * q * r * s * t * u which are relatively prime to p+q+r+s+t+u. A046306 is the 6-almost primes.
%H Charles R Greathouse IV, <a href="/A110232/b110232.txt">Table of n, a(n) for n = 1..10000</a>
%e 160 is in this sequence because 160 = 2^5 * 5, the sum of whose prime factors is 2 + 2 + 2 + 2 + 2 + 5 = 15 = 3 * 5, which has a prime factor in common with 160.
%o (PARI) list(lim)=my(v=List()); forprime(p=2, lim\16, forprime(q=2, min(p, lim\8\p), my(pq=p*q); forprime(r=2, min(lim\pq\4, q), my(pqr=pq*r); forprime(s=2, min(lim\pqr\2, r), my(pqrs=pqr*s); forprime(t=2,min(lim\pqrs,s), my(pqrst=pqrs*t,n); forprime(u=2,min(lim\pqrst,t), n=pqrst*u; if(gcd(n, p+q+r+s+t+u)>1, listput(v, n)))))))); Set(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y Cf. A046306, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110289, A110290, A110296, A110297.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jul 17 2005
%E Extended by _Ray Chandler_, Jul 20 2005
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