A110296 8-almost primes p*q*r*s*t*u*v*w relatively prime to p+q+r+s+t+u+v+w.

384, 640, 864, 1408, 1664, 2016, 2176, 2400, 2432, 2944, 3240, 3712, 3744, 3968, 4374, 4536, 4736, 5248, 5280, 5472, 5504, 5600, 6016, 6240, 6784, 7128, 7392, 7552, 7808, 7840, 8424, 8576, 8800, 8928, 9088, 9120, 9344, 10112, 10400, 10584, 10624

Offset

1,1

Comments

The primes p, q, r, s, t, u, v, w are not necessarily distinct. The 8-almost primes are A046310. The converse, A110297, is 8-almost primes p*q*r*s*t*u*v*w which are not relatively prime to p+q+r+s+t+u+v+w.

Links

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

Example

864 is an element of this sequence because 864 = 2^5 * 3^3, so the sum of prime factors is 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 = 19 which is prime, hence relatively prime to 864. That is the same sum of prime factors as 640 = 2^7 * 5, hence 640 is also a member of this sequence. The sum of prime factors need not be prime for this membership, for example, 2432 = 2^7 * 19 has sum of prime factors 2 + 2 + 2 + 2 + 2 + 2 + 2 + 19 = 33 = 3 * 11, which is composite, yet relatively prime to 2432.

Prog

(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

Crossrefs

Cf. A046310, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110297.

Sequence in context: A342065 A046491 A046492 * A179664 A212430 A134175

Adjacent sequences: A110293 A110294 A110295 * A110297 A110298 A110299

Keyword

easy,nonn

Author

Jonathan Vos Post, Jul 18 2005

Extensions

Corrected and extended by Ray Chandler, Jul 20 2005

Status

approved