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Greatest prime factor of n and its direct neighbors.
8

%I #12 Jul 13 2013 12:03:12

%S 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 13,29,29,31,31,31,17,17,17,37,37,37,19,41,41,43,43,43,23,47,47,47,7,

%U 17,17,53,53,53,11,19,29,59,59,61,61,61,31,13,13,67,67,67,23,71,71,73

%N Greatest prime factor of n and its direct neighbors.

%C a(n) = A006530(n + A093075(n));

%C a(n) = max{A006530(n-1), A006530(n), A006530(n+1)}, n>1;

%C a(n) = A006530(A007531(n+1)), n>1;

%C 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 (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 Reinhard Zumkeller, <a href="/A093074/b093074.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) > 47 if n > 212381. - _Charles R Greathouse IV_, Feb 19 2013

%o (Haskell)

%o a093074 1 = 2

%o a093074 n = maximum $ map a006530 [n-1..n+1]

%o -- _Reinhard Zumkeller_, Jul 04 2012

%o (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 Cf. A074399, A190136.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 18 2004