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%I #12 Apr 30 2018 16:34:34
%S 128,192,288,480,648,672,800,1008,1056,1080,1120,1200,1248,1458,1512,
%T 1568,1620,1632,1760,1800,1824,1872,2080,2187,2208,2376,2430,2464,
%U 2520,2640,2720,2736,2784,2800,2808,2912,2976,3000,3040,3402,3528,3552,3564
%N 7-almost primes p*q*r*s*t*u*v not relatively prime to p+q+r+s+t+u+v.
%C The primes p, q, r, s, t, u, v are not necessarily distinct. The 7-almost primes are A046308. The converse, A110289, is 7-almost primes p*q*r*s*t*u*v which are relatively prime to p+q+r+s+t+u+v.
%H Harvey P. Dale, <a href="/A110290/b110290.txt">Table of n, a(n) for n = 1..1000</a>
%e 800 = 2^5 * 5^2 is in this sequence because the sum of prime factors 2 + 2 + 2 + 2 + 2 + 5 + 5 = 20 is not relatively prime to 800 (in fact, it is a divisor of 800).
%t Select[Range[4000],PrimeOmega[#]==7&&!CoprimeQ[Total[Flatten[Table[ #[[1]], #[[2]]]&/@ FactorInteger[#]]],#]&] (* _Harvey P. Dale_, Apr 30 2018 *)
%o (PARI) sopfr(n)=local(f);if(n<1,0,f=factor(n);sum(k=1,matsize(f)[1],f[k,1]*f[k,2])) for(n=1,4000,if(bigomega(n)==7&&gcd(n, sopfr(n))>1,print1(n,","))) (Shepherd)
%Y Cf. A046308, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110296, A110297.
%Y Cf. A001414 (sopfr(n)).
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Jul 18 2005
%E Extended by _Ray Chandler_ and _Rick L. Shepherd_, Jul 20 2005
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