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A096919 Greatest prime factor of n-th product of 3 distinct primes.

%I A096919 #17 Nov 03 2024 02:03:51
%S A096919 5,7,11,7,13,17,7,11,19,13,23,11,11,17,29,13,31,19,13,37,23,11,17,41,
%T A096919 17,43,19,13,47,19,13,29,31,53,23,23,59,17,61,37,17,11,19,67,29,41,19,
%U A096919 71,13,43,31,29,73,17,13,31,47,79,23,19,83,23,37,53,89,37,17,41,97,59
%N A096919 Greatest prime factor of n-th product of 3 distinct primes.
%H A096919 Amiram Eldar, <a href="/A096919/b096919.txt">Table of n, a(n) for n = 1..10000</a>
%F A096919 A096917(n)*A096918(n)*a(n) = A007304(n).
%F A096919 A096917(n) < A096918(n) < a(n).
%F A096919 a(n) = A006530(A007304(n)).
%t A096919 f[n_]:=Last/@FactorInteger[n]=={1,1,1};f1[n_]:=Min[First/@FactorInteger[n]];f2[n_]:=Max[First/@FactorInteger[n]];lst={};Do[If[f[n],AppendTo[lst,f2[n]]],{n,0,7!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 10 2010 *)
%o A096919 (Python)
%o A096919 from math import isqrt
%o A096919 from sympy import primepi, primerange, integer_nthroot, primefactors
%o A096919 def A096919(n):
%o A096919     def f(x): return int(n+x-sum(primepi(x//(k*m))-b for a,k in enumerate(primerange(integer_nthroot(x,3)[0]+1),1) for b,m in enumerate(primerange(k+1,isqrt(x//k)+1),a+1)))
%o A096919     def bisection(f,kmin=0,kmax=1):
%o A096919         while f(kmax) > kmax: kmax <<= 1
%o A096919         while kmax-kmin > 1:
%o A096919             kmid = kmax+kmin>>1
%o A096919             if f(kmid) <= kmid:
%o A096919                 kmax = kmid
%o A096919             else:
%o A096919                 kmin = kmid
%o A096919         return kmax
%o A096919     return max(primefactors(bisection(f))) # _Chai Wah Wu_, Aug 30 2024
%Y A096919 Cf. A006530, A007304, A096917, A096918.
%K A096919 nonn
%O A096919 1,1
%A A096919 _Reinhard Zumkeller_, Jul 15 2004