A051270 Numbers that are divisible by exactly 5 different primes.

2310, 2730, 3570, 3990, 4290, 4620, 4830, 5460, 5610, 6006, 6090, 6270, 6510, 6630, 6930, 7140, 7410, 7590, 7770, 7854, 7980, 8190, 8580, 8610, 8778, 8970, 9030, 9240, 9282, 9570, 9660, 9690, 9870, 10010, 10230, 10374, 10626, 10710, 10920, 11130, 11220, 11310

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Examples

			2730 = 2*3*5*7*13 is the first nontrivial 5-prime factor number following the 5th primorial, 2310 = 2*3*5*7*11.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Hans Montanus and Ron Westdijk, Cellular Automation and Binomials, Green Blue Mathematics (2022), p. 90.

Crossrefs

A046303 is a subsequence.

Row 5 of A125666.

Cf. A000977, A002110.

Programs

Maple

A051270 := proc(n)
    option remember;
    local a;
    if n = 1 then
        2*3*5*7*11 ;
    else
        for a from procname(n-1)+1 do
            if A001221(a)= 5 then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Oct 13 2019

Mathematica

Select[Range[12000],PrimeNu[#]==5&] (* Harvey P. Dale, Feb 13 2012 *)

PARI

is(n)=omega(n)==5 \\ Charles R Greathouse IV, Apr 29 2015

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=5)=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

Python

from sympy import primefactors
print([n for n in range(2, 20001) if len(primefactors(n))==5]) # Indranil Ghosh, Apr 06 2017