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
Examples
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.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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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
Corrected and extended by Ray Chandler, Jul 20 2005
Comments