A132882 a(n) = the sum of the positive isolated divisors of n.

1, 0, 4, 4, 6, 6, 8, 12, 13, 15, 12, 18, 14, 21, 24, 28, 18, 33, 20, 30, 32, 33, 24, 50, 31, 39, 40, 53, 30, 55, 32, 60, 48, 51, 48, 81, 38, 57, 56, 78, 42, 77, 44, 81, 78, 69, 48, 114, 57, 90, 72, 95, 54, 114, 72, 102, 80, 87, 60, 147, 62, 93, 104, 124, 84, 138, 68, 123, 96

Offset: 1

Author

Leroy Quet, Sep 03 2007

Keywords

• nonn

Comments

A divisor, d, of n is isolated if neither (d-1) nor (d+1) divides n.

The convention for 1 is that it is an isolated divisor iff n is not even. - Olivier Gérard, Sep 22 2007

Examples

			The positive divisors of 56 are: 1,2,4,7,8,14,28,56. Of these, 1 and 2 are adjacent and 7 and 8 are adjacent. The isolated divisors are therefore 4,14, 28,56. So a(56) = 4 +14 +28 +56 = 102.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A132881, A132748.

Programs

Mathematica

Table[Plus@@Select[Divisors[n],(#==1||Mod[n,#-1]>0)&&Mod[n,#+1]>0&],{n,1,200}] (* Olivier Gérard, Sep 22 2007 *)

Formula

a(n) = A000203(n) - A132748(n), where A000203 is sigma(n), sum of divisors of n.

Extensions

More terms from Olivier Gérard, Sep 22 2007