A046389 Products of exactly three distinct odd primes.

105, 165, 195, 231, 255, 273, 285, 345, 357, 385, 399, 429, 435, 455, 465, 483, 555, 561, 595, 609, 615, 627, 645, 651, 663, 665, 705, 715, 741, 759, 777, 795, 805, 861, 885, 897, 903, 915, 935, 957, 969, 987, 1001, 1005, 1015, 1023, 1045, 1065, 1085

Offset

1,1

Comments

The old name was "Odd numbers with exactly 3 distinct prime factors", which is slightly ambiguous, since it might be interpreted to include 315 = 3^2*5*7. Cf. A278569. - N. J. A. Sloane, Nov 27 2016

Links

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

Mathematica

f[n_] := OddQ[n] && Last/@FactorInteger[n]=={1, 1, 1}; lst={}; Do[If[f[n], AppendTo[lst, n]], {n, 2000}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 23 2009 *)

Prog

(PARI) list(lim)=my(v=List(), t); forprime(p=3, lim^(1/3), forprime(q=p+1, sqrt(lim\p), t=p*q; forprime(r=q+1, lim\t, listput(v, t*r)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 26 2011
(Python)
from math import isqrt
from sympy import primepi, integer_nthroot
def A046389(n):
    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
    def f(x): return int(n+x-sum(primepi(x//(k*m))-b for a, k in enumerate(primerange(3, integer_nthroot(x, 3)[0]+1), 2) for b, m in enumerate(primerange(k+1, isqrt(x//k)+1), a+1)))
    return bisection(f, n, n) # Chai Wah Wu, Sep 10 2024

Crossrefs

Cf. A046316, A046405, A007304, A278569.

Sequence in context: A013590 A216918 A278569 * A154430 A118678 A152940

Adjacent sequences: A046386 A046387 A046388 * A046390 A046391 A046392

Keyword

nonn

Author

Patrick De Geest, Jun 15 1998

Extensions

Name clarified by N. J. A. Sloane, Nov 27 2016

Status

approved