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
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Haskell
a046316 n = a046316_list !! (n-1) a046316_list = filter ((== 3) . a001222) [1, 3 ..] -- Reinhard Zumkeller, May 05 2015
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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
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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
Extensions
Definition clarified by N. J. A. Sloane, Dec 19 2017