A046387 Products of exactly 5 distinct primes.

2310, 2730, 3570, 3990, 4290, 4830, 5610, 6006, 6090, 6270, 6510, 6630, 7410, 7590, 7770, 7854, 8610, 8778, 8970, 9030, 9282, 9570, 9690, 9870, 10010, 10230, 10374, 10626, 11130, 11310, 11730, 12090, 12210, 12390, 12558, 12810, 13090, 13110

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• easy
• nonn

Comments

Subsequence of A051270. 4620 = 2^2*3*5*7*11 is in A051270 but not in here, for example. - R. J. Mathar, Nov 10 2014

Examples

			a(1) = 2310 = 2 * 3 * 5 * 7 * 11 = A002110(5) = 5#.
a(2) = 2730 = 2 * 3 * 5 * 7 * 13.
a(3) = 3570 = 2 * 3 * 5 * 7 * 17.
a(10) = 6006 = 2 * 3 * 7 * 11 * 13.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Products of exactly k distinct primes, for k = 1 to 6: A000040, A006881. A007304, A046386, A046387, A067885.

Cf. A000040, A000961, A001221, A005117, A000977, A002110, A006881, A007304, A007774, A033992, A033993, A046386.

Cf. A014614, A046403, A051270.

Programs

Maple

A046387 := 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 and issqrfree(a) then
                return a;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Oct 13 2019

Mathematica

f5Q[n_]:=Last/@FactorInteger[n]=={1, 1, 1, 1, 1}; lst={};Do[If[f5Q[n], AppendTo[lst, n]], {n, 8!}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 26 2008 *)

PARI

is(n)=factor(n)[,2]==[1,1,1,1,1]~ \\ Charles R Greathouse IV, Sep 17 2015

PARI

is(n)= omega(n)==5 && bigomega(n)==5 \\ Hugo Pfoertner, Dec 18 2018

Python

from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
def A046387(n):
    def g(x,a,b,c,m): yield from (((d,) for d in enumerate(primerange(b+1,isqrt(x//c)+1),a+1)) if m==2 else (((a2,b2),)+d for a2,b2 in enumerate(primerange(b+1,integer_nthroot(x//c,m)[0]+1),a+1) for d in g(x,a2,b2,c*b2,m-1)))
    def f(x): return int(n+x-sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x,0,1,1,5)))
    def bisection(f,kmin=0,kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    return bisection(f) # Chai Wah Wu, Aug 30 2024

Extensions

Entry revised by N. J. A. Sloane, Apr 10 2006