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A046389
Products of exactly three distinct odd primes.
27
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
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, primerange
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
KEYWORD
nonn
AUTHOR
Patrick De Geest, Jun 15 1998
EXTENSIONS
Name clarified by N. J. A. Sloane, Nov 27 2016
STATUS
approved