A110297 8-almost primes p*q*r*s*t*u*v*w not relatively prime to p+q+r+s+t+u+v+w.

256, 576, 896, 960, 1296, 1344, 1440, 1600, 1944, 2112, 2160, 2240, 2496, 2916, 3024, 3136, 3168, 3264, 3360, 3520, 3600, 3648, 4000, 4160, 4416, 4704, 4752, 4860, 4896, 4928, 5040, 5400, 5440, 5568, 5616, 5824, 5952, 6000, 6080, 6561, 6624, 6804, 7056

Offset: 1

Author

Jonathan Vos Post, Jul 18 2005

Keywords

• easy
• nonn

Comments

The primes p, q, r, s, t, u, v, w are not necessarily distinct. The 8-almost primes are A046310. The converse, A110296, is 8-almost primes p*q*r*s*t*u*v*w which are relatively prime to p+q+r+s+t+u+v+w.

Examples

			576 = 2^6 * 3^2 is an element of this sequence because its sum of prime factors is 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 = 18 = 2 * 3^2 which is a factor of 576 and not relatively prime to 576.
		

Links

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

Crossrefs

Cf. A046310, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110296.

Programs

PARI

list(lim)=my(v=List()); forprime(p=2, lim\128, forprime(q=2, min(p, lim\64\p), my(pq=p*q); forprime(r=2, min(lim\pq\32, q), my(pqr=pq*r); forprime(s=2, min(lim\pqr\16, r), my(pqrs=pqr*s); forprime(t=2, min(lim\pqrs\8, s), my(pqrst=pqrs*t); forprime(u=2, min(lim\pqrst\4, t), my(pqrstu=pqrst*u); forprime(w=2,min(lim\pqrstu\2,u), my(pqrstuw=pqrstu*w,n); forprime(x=2,min(lim\pqrstuw,w), n=pqrstuw*x; if(gcd(n, p+q+r+s+t+u+w+x)>1, listput(v, n)))))))))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017

Extensions

Extended by Ray Chandler, Jul 20 2005