%I A110296
%S A110296 384,640,864,1408,1664,2016,2176,2400,2432,2944,3240,3712,3744,3968,
%T A110296 4374,4536,4736,5248,5280,5472,5504,5600,6016,6240,6784,7128,7392,7552,
%U A110296 7808,7840,8424,8576,8800,8928,9088,9120,9344,10112,10400,10584,10624
%N A110296 8-almost primes p*q*r*s*t*u*v*w relatively prime to p+q+r+s+t+u+v+w.
%C A110296 The primes p, q, r, s, t, u, v, w are not necessarily distinct. The 8-almost 
               primes are A046310. The converse, A110297, is 8-almost primes p*q*r*s*t*u*v*w 
               which are not relatively prime to p+q+r+s+t+u+v+w.
%e A110296 864 is an element of this sequence because 864 = 2^5 * 3^3, so the sum 
               of prime factors is 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 = 19 which is prime, 
               hence relatively prime to 864. That is the same sum of prime factors 
               as 640 = 2^7 * 5, hence 640 is also a member of this sequence. The 
               sum of prime factors need not be prime for this membership, for example, 
               2432 = 2^7 * 19 has sum of prime factors 2 + 2 + 2 + 2 + 2 + 2 + 
               2 + 19 = 33 = 3 * 11, which is composite, yet relatively prime to 
               2432.
%Y A110296 Cf. A046310, A110187, A110188, A110227, A110228, A110229, A110230, A110231, 
               A110232, A110289, A110290, A110297.
%Y A110296 Sequence in context: A046014 A046491 A046492 this_sequence A134175 A134241 
               A061403
%Y A110296 Adjacent sequences: A110293 A110294 A110295 this_sequence A110297 A110298 
               A110299
%K A110296 easy,nonn
%O A110296 1,1
%A A110296 Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 18 2005
%E A110296 Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), 
               Jul 20 2005