A110228 4-almost primes p * q * r * s not relatively prime to p + q + r + s.

16, 24, 36, 60, 81, 84, 100, 126, 132, 140, 150, 156, 196, 204, 220, 228, 234, 260, 276, 308, 315, 330, 340, 342, 348, 364, 372, 375, 380, 444, 460, 476, 484, 490, 492, 495, 510, 516, 525, 532, 558, 564, 572, 580, 585, 620, 625, 636, 644, 650, 666, 676, 690

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

Examples

			84 is in this sequence because 84 = 2^2 * 3 * 7 and the sum of these prime factors is 2 + 2 + 3 + 7 = 14 = 2 * 7, which is a divisor of 84.
		

Links

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

Crossrefs

Cf. A014613, A110187, A110188, A110227, 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