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A074400 Sum of the even divisors of 2n.

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