A176655 Numbers that are divisible by exactly 7 distinct primes.

510510, 570570, 690690, 746130, 870870, 881790, 903210, 930930, 1009470, 1021020, 1067430, 1111110, 1138830, 1141140, 1193010, 1217370, 1231230, 1272810, 1291290, 1345890, 1360590, 1381380, 1385670, 1411410, 1438710

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 22 2010

Keywords

• nonn

Examples

			1711710 = 2 * 3^2 * 5 * 7 * 11 * 13 * 19.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Row 7 of A125666.

Cf. A046386, A046387, A067885, A123321.

Programs

Mathematica

Select[Range[9!,5*9! ],Length[FactorInteger[ # ]]==7&]
Select[Range[144*10^4],PrimeNu[#]==7&] (* Harvey P. Dale, Jul 05 2022 *)

PARI

isA176655(n)=omega(n)==7 \\ Charles R Greathouse IV, Mar 11 2011

PARI

(PARI) A246655(lim)=my(v=List(primes([2,lim\=1]))); for(e=2,logint(lim,2), forprime(p=2,sqrtnint(lim,e), listput(v,p^e))); Set(v)
list(lim,pr=7)=if(pr==1, return(A246655(lim))); my(v=List(),pr1=pr-1,mx=prod(i=1,pr1,prime(i))); forprime(p=prime(pr),lim\mx, my(u=list(lim\p,pr1)); for(i=1,#u,listput(v,p*u[i]))); Set(v) \\ Charles R Greathouse IV, Feb 03 2023