A110229 5-almost primes p * q * r * s * t relatively prime to p + q + r + s + t.

48, 80, 108, 112, 176, 208, 252, 272, 300, 304, 368, 405, 420, 464, 468, 496, 500, 567, 592, 656, 660, 675, 684, 688, 752, 848, 891, 924, 944, 976, 980, 1020, 1053, 1072, 1116, 1136, 1140, 1168, 1264, 1300, 1323, 1328, 1332, 1372, 1377, 1424, 1428, 1452

Offset: 1

Author

Jonathan Vos Post, Jul 17 2005

Keywords

• easy
• nonn

Comments

p, q, r, s, t are not necessarily distinct. The converse to this is A110230: 5-almost primes p * q * r * s * t which are not relatively prime to p+q+r+s+t. A014614 is the 5-almost primes.

Examples

			48 is in this sequence because 48 = 2^4 * 3, which has no factors in common with 2 + 2 + 2 + 2 + 3 = 11.
		

Links

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

Crossrefs

Cf. A014614, A002033, A110187, A110188, A110227, A110228, A110230, A110231, A110232, A110289, A110290, A110296, A110297.

Programs

PARI

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

Extensions

Extended by Ray Chandler, Jul 20 2005

Incorrect formula and comment of Sep 2009 related to A002033 deleted - R. J. Mathar, Oct 14 2009