%I #10 Feb 01 2017 09:01:15

%S 96,224,352,360,416,486,504,544,600,608,736,792,810,928,936,992,1000,

%T 1176,1184,1224,1312,1368,1376,1400,1504,1656,1696,1701,1782,1888,

%U 1890,1952,2025,2040,2088,2144,2184,2200,2232,2250,2272,2336,2528,2600,2646

%N 6-almost primes p * q * r * s * t * u 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 A110232: 6-almost primes p * q * r * s * t * u which are not relatively prime to p+q+r+s+t+u. A046306 is the 6-almost primes.

%H Charles R Greathouse IV, <a href="/A110231/b110231.txt">Table of n, a(n) for n = 1..10000</a>

%e 96 is an element of this sequence because 96 = 2^5 * 3, the sum of whose prime factors is 2 + 2 + 2 + 2 + 2 + 3 = 13, which has no prime factors in common with 96.

%o (PARI) list(lim)=my(v=List()); forprime(p=2, lim\32, forprime(q=2, min(p, lim\16\p), my(pq=p*q); forprime(r=2, min(lim\pq\8, q), my(pqr=pq*r); forprime(s=2, min(lim\pqr\4, r), my(pqrs=pqr*s); forprime(t=2,min(lim\pqrs\2,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, A110232, 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