OFFSET
1,1
COMMENTS
Equivalently, a(2n+1) = 2n+1 - (2n+1)/p, where p = A020639(2n+1) is the smallest prime divisor of 2n+1.
The even case is trivial: for 2k the largest difference is k.
Successively greater values of a(n) occur when 2n+1 is prime.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A060681(2n+1)
EXAMPLE
For n=17, 2n+1=35; divisors={1,5,7,35}; differences={4,2,28}; a(17) = largest difference = 28 = 35 - 35/5.
MATHEMATICA
a[n_] := 2n+1-(2n+1)/FactorInteger[2n+1][[1, 1]]
(* Second program: *)
Table[Max@ Differences@ Divisors@ # &[2 n + 1], {n, 66}] (* Michael De Vlieger, Jul 15 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 19 2001
EXTENSIONS
Edited by Dean Hickerson, Jan 22 2002
STATUS
approved