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5-almost primes p * q * r * s * t not relatively prime to p + q + r + s + t.
12

%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