A110290 7-almost primes p*q*r*s*t*u*v not relatively prime to p+q+r+s+t+u+v.

128, 192, 288, 480, 648, 672, 800, 1008, 1056, 1080, 1120, 1200, 1248, 1458, 1512, 1568, 1620, 1632, 1760, 1800, 1824, 1872, 2080, 2187, 2208, 2376, 2430, 2464, 2520, 2640, 2720, 2736, 2784, 2800, 2808, 2912, 2976, 3000, 3040, 3402, 3528, 3552, 3564

Offset: 1

Author

Jonathan Vos Post, Jul 18 2005

Keywords

• easy
• nonn

Comments

The primes p, q, r, s, t, u, v are not necessarily distinct. The 7-almost primes are A046308. The converse, A110289, is 7-almost primes p*q*r*s*t*u*v which are relatively prime to p+q+r+s+t+u+v.

Examples

			800 = 2^5 * 5^2 is in this sequence because the sum of prime factors 2 + 2 + 2 + 2 + 2 + 5 + 5 = 20 is not relatively prime to 800 (in fact, it is a divisor of 800).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A046308, A110187, A110188, A110227, A110228, A110229, A110230, A110231, A110232, A110289, A110296, A110297.

Cf. A001414 (sopfr(n)).

Programs

Mathematica

Select[Range[4000],PrimeOmega[#]==7&&!CoprimeQ[Total[Flatten[Table[ #[[1]], #[[2]]]&/@ FactorInteger[#]]],#]&] (* Harvey P. Dale, Apr 30 2018 *)

PARI

sopfr(n)=local(f);if(n<1,0,f=factor(n);sum(k=1,matsize(f)[1],f[k,1]*f[k,2]))
isok(n)=bigomega(n)==7&&gcd(n, sopfr(n))>1 \\ Rick L. Shepherd, Jul 20 2005

Extensions

Extended by Ray Chandler and Rick L. Shepherd, Jul 20 2005