A110231 6-almost primes p * q * r * s * t * u relatively prime to p+q+r+s+t+u.

96, 224, 352, 360, 416, 486, 504, 544, 600, 608, 736, 792, 810, 928, 936, 992, 1000, 1176, 1184, 1224, 1312, 1368, 1376, 1400, 1504, 1656, 1696, 1701, 1782, 1888, 1890, 1952, 2025, 2040, 2088, 2144, 2184, 2200, 2232, 2250, 2272, 2336, 2528, 2600, 2646

Offset: 1

Author

Jonathan Vos Post, Jul 17 2005

Keywords

• easy
• nonn

Comments

p, q, r, s, t, u are not necessarily distinct. The converse to this is A110232: 6-almost primes p * q * r * s * t * u which are not relatively prime to p+q+r+s+t+u. A046306 is the 6-almost primes.

Examples

			96 is an element of this sequence because 96 = 2^5 * 3, the sum of whose prime factors is 2 + 2 + 2 + 2 + 2 + 3 = 13, which has no prime factors in common with 96.
		

Links

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

Crossrefs

Cf. A046306, A110187, A110188, A110227, A110228, A110229, A110230, A110232, A110289, A110290, A110296, A110297.

Programs

PARI

list(lim)=my(v=List()); forprime(p=2, lim\32, forprime(q=2, min(p, lim\16\p), my(pq=p*q); forprime(r=2, min(lim\pq\8, q), my(pqr=pq*r); forprime(s=2, min(lim\pqr\4, r), my(pqrs=pqr*s); forprime(t=2,min(lim\pqrs\2,s), my(pqrst=pqrs*t,n); forprime(u=2,min(lim\pqrst,t), n=pqrst*u; if(gcd(n, p+q+r+s+t+u)==1, listput(v, n)))))))); Set(v) \\ Charles R Greathouse IV, Jan 31 2017

Extensions

Extended by Ray Chandler, Jul 20 2005