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%I #40 Nov 17 2017 04:14:26
%S 2,6,8,14,12,24,16,30,26,36,24,56,28,48,48,62,36,78,40,84,64,72,48,
%T 120,62,84,80,112,60,144,64,126,96,108,96,182,76,120,112,180,84,192,
%U 88,168,156,144,96,248,114,186,144,196,108,240,144,240,160,180,120,336,124,192
%N Sum of the even divisors of 2n.
%C Also alternating row sums of A236106. - _Omar E. Pol_, Jan 23 2014
%C Could also be called the twice sigma function, see first formula. - _Omar E. Pol_, Feb 05 2014
%H Antti Karttunen, <a href="/A074400/b074400.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F a(n) = 2*sigma(n) = 2*A000203(n).
%F Dirichlet g.f.: 2*zeta(s-1)*zeta(s). - _Ilya Gutkovskiy_, Jul 06 2016
%e The even divisors of 12 are 12, 6, 4, 2, which sum to 24, so a(6) = 24.
%p with(numtheory): seq(2*sigma(n),n=1..65);
%t f[n_] := Plus @@ Select[ Divisors[ 2n], EvenQ]; Array[f, 62] (* _Robert G. Wilson v_, Apr 09 2011 *)
%o (PARI) a(n) = 2 * sigma(n); \\ _Joerg Arndt_, Apr 14 2013
%o (PARI) a(n) = sumdiv(2*n, d, !(d%2) * d); \\ _Michel Marcus_, Jan 23 2014
%Y k times sigma(n), k=1..6: A000203, this sequence, A272027, A239050, A274535, A274536.
%Y Cf. A146076, which includes the zeros for odd n.
%K easy,nonn
%O 1,1
%A _Joseph L. Pe_, Nov 25 2002
%E More terms from _Emeric Deutsch_, May 24 2004
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