A110232 6-almost primes p * q * r * s * t * u not relatively prime to p+q+r+s+t+u.

64, 144, 160, 216, 240, 324, 336, 400, 528, 540, 560, 624, 729, 756, 784, 816, 840, 880, 900, 912, 1040, 1104, 1134, 1188, 1215, 1232, 1260, 1320, 1350, 1360, 1392, 1404, 1456, 1488, 1500, 1520, 1560, 1764, 1776, 1836, 1840, 1848, 1904, 1936, 1960, 1968

Offset: 1

Author

Jonathan Vos Post, Jul 17 2005

Keywords

• easy
• nonn

Comments

p, q, r, s, t, u are not necessarily distinct. The converse to this is A110231: 6-almost primes p * q * r * s * t * u which are relatively prime to p+q+r+s+t+u. A046306 is the 6-almost primes.

Examples

			160 is in this sequence because 160 = 2^5 * 5, the sum of whose prime factors is 2 + 2 + 2 + 2 + 2 + 5 = 15 = 3 * 5, which has a prime factor in common with 160.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046306, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110289, A110290, A110296, A110297.

Programs

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); forprime(t=2,min(lim\pqrs,s), my(pqrst=pqrs*t,n); forprime(u=2,min(lim\pqrst,t), n=pqrst*u; if(gcd(n, p+q+r+s+t+u)>1, listput(v, n)))))))); Set(v) \\ Charles R Greathouse IV, Jan 31 2017

Extensions

Extended by Ray Chandler, Jul 20 2005