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

1,1

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

Links

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

Example

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.

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 *)

Prog

(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

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.

Sequence in context: A285744 A361039 A051270 * A136154 A376380 A258360

Adjacent sequences: A046384 A046385 A046386 * A046388 A046389 A046390

Keyword

easy,nonn

Author

Patrick De Geest, Jun 15 1998

Extensions

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

Status

approved