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%I #12 Aug 30 2024 21:42:07
%S 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 17,43,19,13,47,19,13,29,31,53,23,23,59,17,61,37,17,11,19,67,29,41,19,
%U 71,13,43,31,29,73,17,13,31,47,79,23,19,83,23,37,53,89,37,17,41,97,59
%N Greatest prime factor of n-th product of 3 distinct primes.
%C A096917(n)*A096918(n)*a(n) = A007304(n); A096917(n) < A096918(n) < a(n);
%C a(n) = A006530(A007304(n)).
%t 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 (Python)
%o from math import isqrt
%o from sympy import primepi, primerange, integer_nthroot, primefactors
%o def A096919(n):
%o 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 def bisection(f,kmin=0,kmax=1):
%o while f(kmax) > kmax: kmax <<= 1
%o while kmax-kmin > 1:
%o kmid = kmax+kmin>>1
%o if f(kmid) <= kmid:
%o kmax = kmid
%o else:
%o kmin = kmid
%o return kmax
%o return max(primefactors(bisection(f))) # _Chai Wah Wu_, Aug 30 2024
%K nonn,changed
%O 1,1
%A _Reinhard Zumkeller_, Jul 15 2004
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