A110227 4-almost primes p * q * r * s relatively prime to p + q + r + s.

40, 54, 56, 88, 90, 104, 135, 136, 152, 184, 189, 198, 210, 225, 232, 248, 250, 294, 296, 297, 306, 328, 344, 350, 351, 376, 390, 414, 424, 441, 459, 462, 472, 488, 513, 522, 536, 546, 550, 568, 570, 584, 621, 632, 664, 686, 712, 714, 735, 738, 765, 776

Offset: 1

Author

Jonathan Vos Post, Jul 16 2005

Keywords

• easy
• nonn

Comments

p, q, r, s are not necessarily distinct. The converse to this is A110228: 4-almost primes p * q * r * s not relatively prime to p+q+r+s.

Examples

			104 is in this sequence because 104 = 2^3 * 13, which is relatively prime to 2 + 2 + 2 + 13 = 19, which is prime.
		

Links

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

Crossrefs

Cf. A014613, A110187, A110188, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110296, A110297.

Programs

PARI

list(lim)=my(v=List()); forprime(p=2,lim\8, forprime(q=2,min(p,lim\4\p), my(pq=p*q); forprime(r=2,min(lim\pq\2,q), my(pqr=pq*r,t); forprime(s=2,min(lim\pqr,r), t=pqr*s; if(gcd(t,p+q+r+s)==1, listput(v,t)))))); Set(v) \\ Charles R Greathouse IV, Jan 31 2017

Extensions

Corrected and extended by Ray Chandler, Jul 20 2005