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A093074 Greatest prime factor of n and its direct neighbors.

%I A093074 #12 Jul 13 2013 12:03:12
%S A093074 2,3,3,5,5,7,7,7,5,11,11,13,13,13,7,17,17,19,19,19,11,23,23,23,13,13,
%T A093074 13,29,29,31,31,31,17,17,17,37,37,37,19,41,41,43,43,43,23,47,47,47,7,
%U A093074 17,17,53,53,53,11,19,29,59,59,61,61,61,31,13,13,67,67,67,23,71,71,73
%N A093074 Greatest prime factor of n and its direct neighbors.
%C A093074 a(n) = A006530(n + A093075(n));
%C A093074 a(n) = max{A006530(n-1), A006530(n), A006530(n+1)}, n>1;
%C A093074 a(n) = A006530(A007531(n+1)), n>1;
%C A093074 for all primes p>2: a(p)=a(p-1)=p and if p is not the lesser member of a twin prime pair, then also a(p+1)=p;
%C A093074 (n,n+2) is a twin prime pair iff a(n-1)=a(n)=n and a(n+1)=a(n+2)=a(n+3)=n+2.
%H A093074 Reinhard Zumkeller, <a href="/A093074/b093074.txt">Table of n, a(n) for n = 1..10000</a>
%F A093074 a(n) > 47 if n > 212381. - _Charles R Greathouse IV_, Feb 19 2013
%o A093074 (Haskell)
%o A093074 a093074 1 = 2
%o A093074 a093074 n = maximum $ map a006530 [n-1..n+1]
%o A093074 -- _Reinhard Zumkeller_, Jul 04 2012
%o A093074 (PARI) a(n)=my(p=precprime(n+1));if(p>n-2,p,vecmax(apply(n->vecmax(factor(n)[,1]),[n-1,n,n+1]))) \\ _Charles R Greathouse IV_, Feb 19 2013
%Y A093074 Cf. A074399, A190136.
%K A093074 nonn
%O A093074 1,1
%A A093074 _Reinhard Zumkeller_, Mar 18 2004