Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jan 31 2017 16:53:29
%S 32,72,120,162,168,180,200,243,264,270,280,312,378,392,396,408,440,
%T 450,456,520,552,588,594,612,616,630,680,696,700,702,728,744,750,760,
%U 780,828,882,888,918,920,945,952,968,984,990,1026,1032,1044,1050,1064,1092
%N 5-almost primes p * q * r * s * t not relatively prime to p + q + r + s + t.
%C p, q, r, s, t are not necessarily distinct. The converse to this is A110229: 5-almost primes p * q * r * s * t which are relatively prime to p+q+r+s+t. A014614 is the 5-almost primes.
%H Charles R Greathouse IV, <a href="/A110230/b110230.txt">Table of n, a(n) for n = 1..10000</a>
%e 180 is in this sequence because 180 = 2^2 * 3^2 * 5, the sum of the prime factors being 2 + 2 + 3 + 3 + 5 = 15 = 3 * 5 which has two prime factors in common with 180.
%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,n); forprime(t=2,min(lim\pqrs,s), n=pqrs*t; if(gcd(n, p+q+r+s+t)>1, listput(v, n))))))); Set(v) \\ _Charles R Greathouse IV_, Jan 31 2017
%Y Cf. A014614, A110187, A110188, A110227, A110228, A110229, A110231, 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