cp's OEIS Frontend

A046313 Numbers that are divisible by at least 10 primes (counted with multiplicity).

%I A046313 #22 Aug 24 2024 01:57:44
%S A046313 1024,1536,2048,2304,2560,3072,3456,3584,3840,4096,4608,5120,5184,
%T A046313 5376,5632,5760,6144,6400,6656,6912,7168,7680,7776,8064,8192,8448,
%U A046313 8640,8704,8960,9216,9600,9728,9984,10240,10368,10752,11264,11520,11664,11776
%N A046313 Numbers that are divisible by at least 10 primes (counted with multiplicity).
%H A046313 John Cerkan, <a href="/A046313/b046313.txt">Table of n, a(n) for n = 1..10000</a>
%F A046313 Product p_i^e_i with Sum e_i >= 10.
%F A046313 a(n) = n + O(n (log log n)^8/log n). - _Charles R Greathouse IV_, Apr 07 2017
%t A046313 Select[Range[12000],PrimeOmega[#]>9&] (* _Harvey P. Dale_, Dec 17 2018 *)
%o A046313 (PARI) is(n)=bigomega(n)>9 \\ _Charles R Greathouse IV_, Sep 17 2015
%o A046313 (Python)
%o A046313 from math import isqrt, prod
%o A046313 from sympy import primerange, integer_nthroot, primepi
%o A046313 def A046313(n):
%o A046313     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)))
%o A046313     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(2,10)))
%o A046313     kmin, kmax = 1,2
%o A046313     while f(kmax) >= kmax:
%o A046313         kmax <<= 1
%o A046313     while True:
%o A046313         kmid = kmax+kmin>>1
%o A046313         if f(kmid) < kmid:
%o A046313             kmax = kmid
%o A046313         else:
%o A046313             kmin = kmid
%o A046313         if kmax-kmin <= 1:
%o A046313             break
%o A046313     return kmax # _Chai Wah Wu_, Aug 23 2024
%Y A046313 Subsequence of A033987, A046304, A046305, A046307, A046309, and A046311.
%Y A046313 Cf. A046314.
%K A046313 nonn
%O A046313 1,1
%A A046313 _Patrick De Geest_, Jun 15 1998