A046307 Numbers that are divisible by at least 7 primes (counted with multiplicity).

128, 192, 256, 288, 320, 384, 432, 448, 480, 512, 576, 640, 648, 672, 704, 720, 768, 800, 832, 864, 896, 960, 972, 1008, 1024, 1056, 1080, 1088, 1120, 1152, 1200, 1216, 1248, 1280, 1296, 1344, 1408, 1440, 1458, 1472, 1512, 1536, 1568, 1584, 1600, 1620

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Product p_i^e_i with Sum e_i >= 7.

Mathematica

Select[Range[2000], PrimeOmega[#]>6&] (* Harvey P. Dale, Nov 16 2012 *)

Prog

(PARI) is(n)=bigomega(n)>6 \\ Charles R Greathouse IV, Sep 17 2015
(Python)
from math import prod, isqrt
from sympy import primerange, integer_nthroot, primepi
def A046307(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+primepi(x)+sum(sum(primepi(x//prod(c[1] for c in a))-a[-1][0] for a in g(x, 0, 1, 1, i)) for i in range(2, 7)))
    kmin, kmax = 1, 2
    while f(kmax) >= kmax:
        kmax <<= 1
    while True:
        kmid = kmax+kmin>>1
        if f(kmid) < kmid:
            kmax = kmid
        else:
            kmin = kmid
        if kmax-kmin <= 1:
            break
    return kmax # Chai Wah Wu, Aug 23 2024

Crossrefs

Cf. A046308.

Sequence in context: A109651 A114408 A114418 * A036331 A046308 A110290

Adjacent sequences: A046304 A046305 A046306 * A046308 A046309 A046310

Keyword

nonn

Author

Patrick De Geest, Jun 15 1998

Status

approved