This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A110290 #17 Sep 11 2024 15:21:59 %S A110290 128,192,288,480,648,672,800,1008,1056,1080,1120,1200,1248,1458,1512, %T A110290 1568,1620,1632,1760,1800,1824,1872,2080,2187,2208,2376,2430,2464, %U A110290 2520,2640,2720,2736,2784,2800,2808,2912,2976,3000,3040,3402,3528,3552,3564 %N A110290 7-almost primes p*q*r*s*t*u*v not relatively prime to p+q+r+s+t+u+v. %C A110290 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 A110290 Harvey P. Dale, <a href="/A110290/b110290.txt">Table of n, a(n) for n = 1..1000</a> %e A110290 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 A110290 Select[Range[4000],PrimeOmega[#]==7&&!CoprimeQ[Total[Flatten[Table[ #[[1]], #[[2]]]&/@ FactorInteger[#]]],#]&] (* _Harvey P. Dale_, Apr 30 2018 *) %o A110290 (PARI) sopfr(n)=local(f);if(n<1,0,f=factor(n);sum(k=1,matsize(f)[1],f[k,1]*f[k,2])) %o A110290 isok(n)=bigomega(n)==7&&gcd(n, sopfr(n))>1 \\ _Rick L. Shepherd_, Jul 20 2005 %Y A110290 Cf. A046308, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110296, A110297. %Y A110290 Cf. A001414 (sopfr(n)). %K A110290 easy,nonn %O A110290 1,1 %A A110290 _Jonathan Vos Post_, Jul 18 2005 %E A110290 Extended by _Ray Chandler_ and _Rick L. Shepherd_, Jul 20 2005