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

1,1

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

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

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

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

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

Sequence in context: A002511 A074383 A107505 * A264598 A165607 A109440

Adjacent sequences: A074397 A074398 A074399 * A074401 A074402 A074403

Keyword

easy,nonn

Author

Joseph L. Pe, Nov 25 2002

Extensions

More terms from Emeric Deutsch, May 24 2004

Status

approved