A110187 3-almost primes p * q * r relatively prime to p+q+r.

12, 20, 28, 44, 45, 52, 63, 68, 75, 76, 92, 99, 116, 117, 124, 147, 148, 153, 164, 165, 171, 172, 175, 188, 207, 212, 236, 244, 245, 261, 268, 273, 275, 279, 284, 292, 316, 325, 332, 333, 345, 356, 363, 369, 385, 387, 388, 399, 404, 412, 423, 425, 428, 435

Offset: 1

Author

Jonathan Vos Post, Jul 15 2005

Keywords

• easy
• nonn

Comments

A110188 is the converse, 3-almost primes p * q * r not relatively prime to p+q+r.

Examples

			a(1) = 12 because 12 = 2^2 * 3, which is relatively prime to 2 + 2 + 3 = 7.
30 is not in the sequence, since 30 = 2 * 3 * 5, which is in fact divisible by 2 + 3 + 5 = 10.
92 is in the sequence since 92 = 2^2 x 23, 2 + 2 + 23 = 27 = 3^3, (92, 27) = 1.
		

Links

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

Crossrefs

Cf. A014612, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110290, A110296, A110297.

Programs

Mathematica

Select[Range[500],PrimeOmega[#]==3&&CoprimeQ[#,Total[Times @@@ FactorInteger[ #]]]&] (* Harvey P. Dale, May 15 2019 *)

PARI

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

Extensions

Extended by Ray Chandler, Jul 20 2005