OFFSET
2,1
COMMENTS
Or, largest of all prime factors of the numbers between prime(n) and prime(n+1).
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 *)
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 *)
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], 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'
-- Reinhard Zumkeller, Jun 22 2011
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved