A096917 - OEIS

%I #21 Nov 03 2024 02:03:44

%S 2,2,2,2,2,2,3,2,2,2,2,2,3,2,2,2,2,2,3,2,2,3,2,2,3,2,2,3,2,3,2,2,2,2,

%T 2,3,2,3,2,2,2,5,3,2,2,2,2,2,3,2,2,3,2,2,5,3,2,2,3,2,2,2,2,2,2,3,3,2,

%U 2,2,5,2,2,2,3,2,3,2,3,2,2,3,2,3,2,2,3,5,2,2,2,3,2,5,2,3,2,2,3,2,3,2

%N Smallest prime factor of the n-th product of 3 distinct primes.

%H Amiram Eldar, <a href="/A096917/b096917.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n)*A096918(n)*A096919(n) = A007304(n).

%F a(n) < A096918(n) < A096919(n).

%F a(n) = A020639(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,f1[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 A096917(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 min(primefactors(bisection(f))) # _Chai Wah Wu_, Aug 30 2024

%Y Cf. A020639, A007304, A096918, A096919.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jul 15 2004