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

%I A046323 #13 Sep 10 2024 00:23:49
%S A046323 59049,98415,137781,164025,216513,229635,255879,273375,321489,334611,
%T A046323 360855,373977,382725,426465,452709,455625,505197,535815,557685,
%U A046323 570807,597051,601425,610173,623295,637875,710775,728271,750141,754515,759375
%N A046323 Odd numbers divisible by exactly 10 primes (counted with multiplicity).
%H A046323 John Cerkan, <a href="/A046323/b046323.txt">Table of n, a(n) for n = 1..10000</a>
%t A046323 Select[Range[9,800001,2],PrimeOmega[#]==10&] (* _Harvey P. Dale_, May 26 2013 *)
%o A046323 (Python)
%o A046323 from math import isqrt, prod
%o A046323 from sympy import primerange, integer_nthroot, primepi
%o A046323 def A046323(n):
%o A046323     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 A046323     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)))
%o A046323     def bisection(f,kmin=0,kmax=1):
%o A046323         while f(kmax) > kmax: kmax <<= 1
%o A046323         while kmax-kmin > 1:
%o A046323             kmid = kmax+kmin>>1
%o A046323             if f(kmid) <= kmid:
%o A046323                 kmax = kmid
%o A046323             else:
%o A046323                 kmin = kmid
%o A046323         return kmax
%o A046323     return bisection(f,n,n) # _Chai Wah Wu_, Sep 09 2024
%Y A046323 Cf. A046314.
%K A046323 nonn
%O A046323 1,1
%A A046323 _Patrick De Geest_, Jun 15 1998