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A052248 Greatest prime divisor of all composite numbers between p and next prime. 23

%I

%S 2,3,5,3,7,3,11,13,5,17,19,7,23,17,29,5,31,23,3,37,41,43,47,11,17,53,

%T 3,37,61,43,67,23,73,5,31,79,83,43,89,5,61,3,97,11,103,109,113,19,29,

%U 79,5,83,127,131,89,5,137,139,47,97,151,103,13,157,163,167,173,29,13

%N Greatest prime divisor of all composite numbers between p and next prime.

%C Or, largest of all prime factors of the numbers between prime(n) and prime(n+1).

%C a(n) = 3, 5, 7, 11, 13 iff prime(n) is in A059960, A080185, A080186, A080187, A080188 respectively. This sequence defines a mapping f of primes > 2 to primes (cf. A080189) and f(p) < p holds for all p > 2. - _Klaus Brockhaus_, Feb 10 2003

%C a(n) = A006530(A061214(n)). - _Reinhard Zumkeller_, Jun 22 2011

%H T. D. Noe, <a href="/A052248/b052248.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = max(prime(n) < k < prime(n+1), A006530(k)).

%e a(8) = 11 since 20 = 2*2*5, 21 = 3*7, 22 = 2*11 are the numbers between prime(8) = 19 and prime(9) = 23.

%e For n=9, n-th prime is 23, composites between 23 and next prime are 24 25 26 27 29 of which largest prime divisor is 13, so a(9)=13.

%t g[n_] := Block[{t = Range[Prime[n] + 1, Prime[n + 1] - 1]}, Max[First /@ Flatten[ FactorInteger@t, 1]]]; Table[ g[n], {n, 2, 72}] (* _Robert G. Wilson v_, Feb 08 2006 *)

%o (PARI) forprime(p=3,360,q=nextprime(p+1); m=0; for(j=p+1,q-1,f=factor(j); a=f[matsize(f)[1],1]; if(m<a,m=a)); print1(m,","))

%o (Haskell)

%o a052248 n = a052248_list !! (n-2)

%o a052248_list = f a065091_list where

%o f (p:ps'@(p':ps)) = (maximum $ map a006530 [p+1..p'-1]) : f ps'

%o -- _Reinhard Zumkeller_, Jun 22 2011

%Y Cf. A006530, A059960, A080185, A080186, A080187, A080188, A080189, A052180, A065091.

%K nonn,easy,nice

%O 2,1

%A _N. J. A. Sloane_

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)