A060685 Largest difference between consecutive divisors (ordered by size) of 2n+1.

2, 4, 6, 6, 10, 12, 10, 16, 18, 14, 22, 20, 18, 28, 30, 22, 28, 36, 26, 40, 42, 30, 46, 42, 34, 52, 44, 38, 58, 60, 42, 52, 66, 46, 70, 72, 50, 66, 78, 54, 82, 68, 58, 88, 78, 62, 76, 96, 66, 100, 102, 70, 106, 108, 74, 112, 92, 78, 102, 110, 82, 100, 126, 86, 130, 114

Offset: 1

Author

Labos Elemer, Apr 19 2001

Keywords

• nonn

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.

Examples

			For n=17, 2n+1=35; divisors={1,5,7,35}; differences={4,2,28}; a(17) = largest difference = 28 = 35 - 35/5.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A060681.

Programs

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 *)

Formula

a(n) = A060681(2n+1)

Extensions

Edited by Dean Hickerson, Jan 22 2002