A132748 a(n) = the sum of the positive non-isolated divisors of n.

0, 3, 0, 3, 0, 6, 0, 3, 0, 3, 0, 10, 0, 3, 0, 3, 0, 6, 0, 12, 0, 3, 0, 10, 0, 3, 0, 3, 0, 17, 0, 3, 0, 3, 0, 10, 0, 3, 0, 12, 0, 19, 0, 3, 0, 3, 0, 10, 0, 3, 0, 3, 0, 6, 0, 18, 0, 3, 0, 21, 0, 3, 0, 3, 0, 6, 0, 3, 0, 3, 0, 27, 0, 3, 0, 3, 0, 6, 0, 12, 0, 3, 0, 23, 0, 3, 0, 3, 0, 36, 0, 3, 0, 3, 0, 10, 0, 3

Offset: 1

Author

Leroy Quet, Aug 27 2007

Keywords

• nonn

Comments

A divisor, d, of n is non-isolated if either (d-1) or (d+1) divides n.

a(2n-1) = 0 for all n >= 1.

Examples

			The positive divisors of 20 are 1,2,4,5,10,20. Of these, 1 and 2 are next to each other and 4 and 5 are next to each other. So a(20) = 1+2+4+5 = 12.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A129308, A132747, A133565.

Programs

Mathematica

Table[Plus @@ (Select[Divisors[n], If[ # > 1,Mod[n, #*(# - 1)] == 0] || Mod[n, #*(# + 1)] == 0 &]), {n, 1, 80}] (* Stefan Steinerberger, Nov 01 2007 *)

PARI

A132748(n) = sumdiv(n,d,((!(n%(1+d)))||((d>1)&&(!(n%(d-1)))))*d); \\ Antti Karttunen, Dec 19 2018

Formula

a(n) = A000203(n) - A132882(n), where A000203 is sigma(n), sum of divisors of n.

Extensions

More terms from Stefan Steinerberger, Nov 01 2007

Extended by Ray Chandler, Jun 24 2008