A046316 Numbers of the form p*q*r where p,q,r are (not necessarily distinct) odd primes.

27, 45, 63, 75, 99, 105, 117, 125, 147, 153, 165, 171, 175, 195, 207, 231, 245, 255, 261, 273, 275, 279, 285, 325, 333, 343, 345, 357, 363, 369, 385, 387, 399, 423, 425, 429, 435, 455, 465, 475, 477, 483, 507, 531, 539, 549, 555, 561, 575, 595, 603, 605

Offset

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Prog

(Haskell)
a046316 n = a046316_list !! (n-1)
a046316_list = filter ((== 3) . a001222) [1, 3 ..]
-- Reinhard Zumkeller, May 05 2015
(PARI) list(lim)=my(v=List(), pq); forprime(p=3, lim\9, forprime(q=3, min(lim\3\p, p), pq=p*q; forprime(r=3, lim\pq, listput(v, pq*r)))); Set(v) \\ Charles R Greathouse IV, Aug 23 2017
(Python)
from math import isqrt
from sympy import primepi, primerange, integer_nthroot
def A046316(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+1 for a, k in enumerate(primerange(3, integer_nthroot(x, 3)[0]+1), 2) for b, m in enumerate(primerange(k, isqrt(x//k)+1), a)))
    return bisection(f, n, n) # Chai Wah Wu, Oct 18 2024

Crossrefs

A369979 sorted into ascending order.

Subsequence of A014612 and of A046340.

Cf. A255646 (final digits), A369054, A369058 (characteristic function), A369252 [= A003415(a(n))].

Subsequences: A046389, A046373, A046405, A075814, A338469, A338556, A338557, A369246.

Sequence in context: A307373 A121614 A046340 * A046373 A228057 A113481

Adjacent sequences: A046313 A046314 A046315 * A046317 A046318 A046319

Keyword

nonn,easy

Author

Patrick De Geest, Jun 15 1998

Extensions

Definition clarified by N. J. A. Sloane, Dec 19 2017

Status

approved