A096919 - OEIS

%I #17 Nov 03 2024 02:03:51

%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.

%H Amiram Eldar, <a href="/A096919/b096919.txt">Table of n, a(n) for n = 1..10000</a>

%F A096917(n)*A096918(n)*a(n) = A007304(n).

%F A096917(n) < A096918(n) < a(n).

%F 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

%Y Cf. A006530, A007304, A096917, A096918.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 15 2004