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

1,2

Links

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

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A283362 A337524 A324047 * A324202 A278240 A263077

Adjacent sequences: A091815 A091816 A091817 * A091819 A091820 A091821

Keyword

easy,nonn

Author

Mohammad K. Azarian, Mar 07 2004

Extensions

More terms from Michel Marcus, Jan 14 2014

Status

approved