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 A052248 Greatest prime divisor of all composite numbers between p and next prime. 23
 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, 3, 37, 61, 43, 67, 23, 73, 5, 31, 79, 83, 43, 89, 5, 61, 3, 97, 11, 103, 109, 113, 19, 29, 79, 5, 83, 127, 131, 89, 5, 137, 139, 47, 97, 151, 103, 13, 157, 163, 167, 173, 29, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Or, largest of all prime factors of the numbers between prime(n) and prime(n+1). 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 a(n) = A006530(A061214(n)). - Reinhard Zumkeller, Jun 22 2011 LINKS T. D. Noe, Table of n, a(n) for n = 2..1000 FORMULA a(n) = max(prime(n) < k < prime(n+1), A006530(k)). EXAMPLE 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. 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. MATHEMATICA 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 *) PROG (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]; if(m

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Last modified August 19 04:10 EDT 2019. Contains 326109 sequences. (Running on oeis4.)