A046304 Divisible by at least 5 primes (counted with multiplicity).

32, 48, 64, 72, 80, 96, 108, 112, 120, 128, 144, 160, 162, 168, 176, 180, 192, 200, 208, 216, 224, 240, 243, 252, 256, 264, 270, 272, 280, 288, 300, 304, 312, 320, 324, 336, 352, 360, 368, 378, 384, 392, 396, 400, 405, 408, 416, 420, 432, 440, 448, 450, 456

Offset

1,1

Links

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

Formula

Product p_i^e_i with Sum e_i >= 5.

a(n) = n + O(n (log log n)^3/log n). - Charles R Greathouse IV, Apr 07 2017

Mathematica

Select[Range[500], PrimeOmega[#]>4&] (* Harvey P. Dale, Apr 16 2013 *)

Prog

(PARI) is(n)=bigomega(n)>4 \\ Charles R Greathouse IV, Sep 17 2015
(Python)
from math import prod, isqrt
from sympy import primerange, primepi, integer_nthroot
def A046304(n):
    def bisection(f, kmin=0, kmax=1):
        while f(kmax) > kmax: kmax <<= 1
        kmin = kmax >> 1
        while kmax-kmin > 1:
            kmid = kmax+kmin>>1
            if f(kmid) <= kmid:
                kmax = kmid
            else:
                kmin = kmid
        return kmax
    def almostprimepi(n, k):
        if k==0: return int(n>=1)
        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)))
        return int(sum(primepi(n//prod(c[1] for c in a))-a[-1][0] for a in g(n, 0, 1, 1, k)) if k>1 else primepi(n))
    def f(x): return n+1+sum(almostprimepi(x, k) for k in range(1, 5))
    return bisection(f, n, n) # Chai Wah Wu, Mar 29 2025

Crossrefs

Subsequence of A033987.

Cf. A014614.

Sequence in context: A114406 A271784 A114416 * A114447 A090052 A163285

Adjacent sequences: A046301 A046302 A046303 * A046305 A046306 A046307

Keyword

nonn

Author

Patrick De Geest, Jun 15 1998

Status

approved