

A093074


Greatest prime factor of n and its direct neighbors.


8



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, 13, 29, 29, 31, 31, 31, 17, 17, 17, 37, 37, 37, 19, 41, 41, 43, 43, 43, 23, 47, 47, 47, 7, 17, 17, 53, 53, 53, 11, 19, 29, 59, 59, 61, 61, 61, 31, 13, 13, 67, 67, 67, 23, 71, 71, 73
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OFFSET

1,1


COMMENTS

a(n) = A006530(n + A093075(n));
a(n) = max{A006530(n1), A006530(n), A006530(n+1)}, n>1;
a(n) = A006530(A007531(n+1)), n>1;
for all primes p>2: a(p)=a(p1)=p and if p is not the lesser member of a twin prime pair, then also a(p+1)=p;
(n,n+2) is a twin prime pair iff a(n1)=a(n)=n and a(n+1)=a(n+2)=a(n+3)=n+2.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


FORMULA

a(n) > 47 if n > 212381.  Charles R Greathouse IV, Feb 19 2013


PROG

(Haskell)
a093074 1 = 2
a093074 n = maximum $ map a006530 [n1..n+1]
 Reinhard Zumkeller, Jul 04 2012
(PARI) a(n)=my(p=precprime(n+1)); if(p>n2, p, vecmax(apply(n>vecmax(factor(n)[, 1]), [n1, n, n+1]))) \\ Charles R Greathouse IV, Feb 19 2013


CROSSREFS

Cf. A074399, A190136.
Sequence in context: A185075 A074399 A090302 * A284412 A136548 A007917
Adjacent sequences: A093071 A093072 A093073 * A093075 A093076 A093077


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Mar 18 2004


STATUS

approved



