A074400 Sum of the even divisors of 2n.

2, 6, 8, 14, 12, 24, 16, 30, 26, 36, 24, 56, 28, 48, 48, 62, 36, 78, 40, 84, 64, 72, 48, 120, 62, 84, 80, 112, 60, 144, 64, 126, 96, 108, 96, 182, 76, 120, 112, 180, 84, 192, 88, 168, 156, 144, 96, 248, 114, 186, 144, 196, 108, 240, 144, 240, 160, 180, 120, 336, 124, 192

Offset: 1

Author

Joseph L. Pe, Nov 25 2002

Keywords

• easy
• nonn

Comments

Also alternating row sums of A236106. - Omar E. Pol, Jan 23 2014

Could also be called the twice sigma function, see first formula. - Omar E. Pol, Feb 05 2014

Examples

			The even divisors of 12 are 12, 6, 4, 2, which sum to 24, so a(6) = 24.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sigma(n)
• Index entries for sequences related to sums of divisors

Crossrefs

k times sigma(n), k=1..6: A000203, this sequence, A272027, A239050, A274535, A274536.

Cf. A146076, which includes the zeros for odd n.

Programs

Maple

with(numtheory): seq(2*sigma(n),n=1..65);

Mathematica

f[n_] := Plus @@ Select[ Divisors[ 2n], EvenQ]; Array[f, 62] (* Robert G. Wilson v, Apr 09 2011 *)

PARI

a(n) = 2 * sigma(n); \\ Joerg Arndt, Apr 14 2013

PARI

a(n) = sumdiv(2*n, d, !(d%2) * d); \\ Michel Marcus, Jan 23 2014

Formula

a(n) = 2*sigma(n) = 2*A000203(n).

Dirichlet g.f.: 2*zeta(s-1)*zeta(s). - Ilya Gutkovskiy, Jul 06 2016

Extensions

More terms from Emeric Deutsch, May 24 2004