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A162022 Smallest prime factor of n-th odd composite integers A071904.

%I A162022 #16 Aug 01 2024 01:30:04
%S A162022 3,3,3,5,3,3,5,3,3,7,3,5,3,3,5,3,3,7,3,5,3,7,3,5,3,3,3,5,3,7,11,3,5,3,
%T A162022 7,3,3,11,5,3,3,5,3,7,3,13,3,5,3,3,5,11,3,3,3,7,5,3,11,3,5,7,3,13,3,3,
%U A162022 5,3,3,5,13,3,11,3,7,3,5,3,3,5,3,3,7,17,3,5,3,13,7,3,5,3,3,11,3,17,5,3,7,3
%N A162022 Smallest prime factor of n-th odd composite integers A071904.
%C A162022 Records are for n's such that A071904(n) = squares of primes.
%C A162022 a(n) = A020639(A071904(n)). [_Reinhard Zumkeller_, Oct 10 2011]
%H A162022 Reinhard Zumkeller, <a href="/A162022/b162022.txt">Table of n, a(n) for n = 1..10000</a>
%e A162022 A071904(1)=9, hence a(1)=3, A071904(4)=25, hence a(4)=5.
%t A162022 nn=501;With[{ci=Complement[Range[9,nn,2],Prime[Range[PrimePi[nn]]]]}, FactorInteger[ #][[1,1]]&/@ci] (* _Harvey P. Dale_, Nov 30 2012 *)
%o A162022 (Python)
%o A162022 from sympy import primepi, primefactors
%o A162022 def A162022(n):
%o A162022     if n == 1: return 3
%o A162022     m, k = n, primepi(n) + n + (n>>1)
%o A162022     while m != k:
%o A162022         m, k = k, primepi(k) + n + (k>>1)
%o A162022     return min(primefactors(m)) # _Chai Wah Wu_, Jul 31 2024
%Y A162022 Cf. A014076, A071904.
%K A162022 nonn
%O A162022 1,1
%A A162022 _Zak Seidov_, Jun 25 2009
%E A162022 Corrected example a(4)=5 Francesco Antoni (francesco_antoni(AT)yahoo.com), Aug 04 2010