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A052248
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Greatest prime divisor of all composite numbers between p and next prime.
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23
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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
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OFFSET
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2,1
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COMMENTS
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Or, largest of all prime factors of the numbers between prime(n) and prime(n+1).
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LINKS
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FORMULA
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a(n) = max(prime(n) < k < prime(n+1), A006530(k)).
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
cmp[{a_, b_}]:=Max[Flatten[FactorInteger/@Range[a+1, b-1], 1][[All, 1]]]; cmp/@ Partition[ Prime[Range[2, 80]], 2, 1] (* Harvey P. Dale, May 16 2020 *)
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PROG
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(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, ", "))
(Haskell)
a052248 n = a052248_list !! (n-2)
a052248_list = f a065091_list where
f (p:ps'@(p':ps)) = (maximum $ map a006530 [p+1..p'-1]) : f ps'
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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STATUS
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approved
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