A060684 Smallest difference between consecutive divisors (ordered by size) of 2n+1.

2, 4, 6, 2, 10, 12, 2, 16, 18, 2, 22, 4, 2, 28, 30, 2, 2, 36, 2, 40, 42, 2, 46, 6, 2, 52, 4, 2, 58, 60, 2, 4, 66, 2, 70, 72, 2, 4, 78, 2, 82, 4, 2, 88, 6, 2, 4, 96, 2, 100, 102, 2, 106, 108, 2, 112, 4, 2, 6, 10, 2, 4, 126, 2, 130, 6, 2, 136, 138, 2, 2, 4, 2, 148, 150, 2, 4, 156, 2, 6

Offset: 1

Author

Labos Elemer, Apr 19 2001

Keywords

• nonn

Comments

Successively greater values of a(n) occur when 2n+1 is prime.

Examples

			For n=38, 2n+1=77; divisors={1,7,11,77}; differences={6,4,66}; a(38) = smallest difference = 4.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A060680.

Different from A071294.

Cf. A193829, A027750.

Programs

Haskell

a060684 = minimum . a193829_row . (+ 1) . (* 2)
-- Reinhard Zumkeller, Jun 25 2015

Mathematica

a[n_ ] := Min@@(Drop[d=Divisors[2n+1], 1]-Drop[d, -1])
Array[Min[Differences[Divisors[2*#+1]]]&,80] (* Harvey P. Dale, Dec 08 2013 *)

Formula

A060680(2n+1)

Extensions

Edited by Dean Hickerson, Jan 22 2002