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

1,2

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.

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A129308, A132747, A133565.

Sequence in context: A356205 A100258 A045763 * A022901 A348215 A331739

Adjacent sequences: A132745 A132746 A132747 * A132749 A132750 A132751

Keyword

nonn

Author

Leroy Quet, Aug 27 2007

Extensions

More terms from Stefan Steinerberger, Nov 01 2007

Extended by Ray Chandler, Jun 24 2008

Status

approved