A091818 Sum of the even proper divisors of 2n. Sum of the even divisors of 2n that are less than 2n.

0, 2, 2, 6, 2, 12, 2, 14, 8, 16, 2, 32, 2, 20, 18, 30, 2, 42, 2, 44, 22, 28, 2, 72, 12, 32, 26, 56, 2, 84, 2, 62, 30, 40, 26, 110, 2, 44, 34, 100, 2, 108, 2, 80, 66, 52, 2, 152, 16, 86, 42, 92, 2, 132, 34, 128, 46, 64, 2, 216, 2, 68, 82, 126, 38, 156, 2, 116

Offset: 1

Author

Mohammad K. Azarian, Mar 07 2004

Keywords

• easy
• nonn

Examples

			The sum of the even divisors of 18 that are less than 18 is 8 = 2+6.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A001065, A032741, A091570, A074400, A173455.

Programs

Mathematica

Table[Total[Select[Most[Divisors[2 n]],EvenQ]],{n,70}] (* Harvey P. Dale, Apr 28 2023 *)

PARI

a(n) = sumdiv(2*n, d, !(d%2) * d * (d<2*n)); \\ Michel Marcus, Jan 14 2014

Python

from sympy import divisors
def a(n): return sum(d for d in divisors(2*n) if d%2==0) - 2*n
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Oct 30 2017

Formula

a(n) = A074400(2n) - 2n. - Michel Marcus, Jan 14 2014

a(n) = Sum_{d|2n, d<2n, d even} d. - Wesley Ivan Hurt, Mar 02 2022

a(n) = 2 * A001065(n). - Alois P. Heinz, Mar 02 2022

Extensions

More terms from Michel Marcus, Jan 14 2014