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 A046311 Numbers that are divisible by at least 9 primes (counted with multiplicity). 4
 512, 768, 1024, 1152, 1280, 1536, 1728, 1792, 1920, 2048, 2304, 2560, 2592, 2688, 2816, 2880, 3072, 3200, 3328, 3456, 3584, 3840, 3888, 4032, 4096, 4224, 4320, 4352, 4480, 4608, 4800, 4864, 4992, 5120, 5184, 5376, 5632, 5760, 5832, 5888, 6048, 6144 (list; graph; refs; listen; history; text; internal format)
 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 >= 9. a(n) = n + O(n (log log n)^7/log n). - Charles R Greathouse IV, Apr 07 2017 MATHEMATICA Select[Range[6200], PrimeOmega[#]>8&] (* Harvey P. Dale, May 20 2013 *) PROG (PARI) is(n)=bigomega(n)>8 \\ Charles R Greathouse IV, Sep 17 2015 (Python) from math import isqrt, prod from sympy import primerange, integer_nthroot, primepi def A046311(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+1+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, 9))) 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 CROSSREFS Subsequence of A033987, A046304, A046305, A046307, and A046309. Cf. A046312. Sequence in context: A234136 A248536 A202461 * A036333 A046312 A045033 Adjacent sequences: A046308 A046309 A046310 * A046312 A046313 A046314 KEYWORD nonn,changed AUTHOR Patrick De Geest, Jun 15 1998 STATUS approved

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Last modified September 19 09:52 EDT 2024. Contains 376008 sequences. (Running on oeis4.)