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

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Hans Montanus and Ron Westdijk, Cellular Automation and Binomials, Math around the Block (2022), p. 90.

Example

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

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 *)

Prog

(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

Crossrefs

A046303 is a subsequence.

Row 5 of A125666.

Cf. A000977, A002110.

Sequence in context: A285487 A285744 A361039 * A046387 A136154 A258360

Adjacent sequences: A051267 A051268 A051269 * A051271 A051272 A051273

Keyword

nonn

Author

Labos Elemer

Status

approved