A046323 Odd numbers divisible by exactly 10 primes (counted with multiplicity).

59049, 98415, 137781, 164025, 216513, 229635, 255879, 273375, 321489, 334611, 360855, 373977, 382725, 426465, 452709, 455625, 505197, 535815, 557685, 570807, 597051, 601425, 610173, 623295, 637875, 710775, 728271, 750141, 754515, 759375

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046314.

Programs

Mathematica

Select[Range[9,800001,2],PrimeOmega[#]==10&] (* Harvey P. Dale, May 26 2013 *)

Python

from math import isqrt, prod
from sympy import primerange, integer_nthroot, primepi
def A046323(n):
    def g(x,a,b,c,m): yield from (((d,) for d in enumerate(primerange(b,isqrt(x//c)+1),a)) if m==2 else (((a2,b2),)+d for a2,b2 in enumerate(primerange(b,integer_nthroot(x//c,m)[0]+1),a) 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,1,3,1,10)))
    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,n,n) # Chai Wah Wu, Sep 09 2024