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%I #56 Aug 07 2022 07:44:58
%S 3,7,12,15,18,28,24,31,39,42,36,60,42,56,72,63,54,91,60,90,96,84,72,
%T 124,93,98,120,120,90,168,96,127,144,126,144,195,114,140,168,186,126,
%U 224,132,180,234,168,144,252,171,217,216,210,162,280,216,248,240,210
%N Sum of divisors of 2*n.
%C a(n) is also the total number of parts in all partitions of 2*n into equal parts. - _Omar E. Pol_, Feb 14 2021
%H N. J. A. Sloane, <a href="/A062731/b062731.txt">Table of n, a(n) for n = 1..20000</a> [First 1000 terms from Harry J. Smith]
%F a(n) = A000203(2*n). - _R. J. Mathar_, Apr 06 2011
%F a(n) = A000203(n) + A054785(n). - _R. J. Mathar_, May 19 2020
%F From _Vaclav Kotesovec_, Aug 07 2022: (Start)
%F Dirichlet g.f.: zeta(s) * zeta(s-1) * (3 - 2^(1-s)).
%F Sum_{k=1..n} a(k) ~ 5 * Pi^2 * n^2 / 24. (End)
%t lst={};Do[AppendTo[lst, DivisorSigma[1, n]], {n, 2, 6!, 2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 20 2008 *)
%t DivisorSigma[1,2*Range[60]] (* _Harvey P. Dale_, Jun 08 2022 *)
%o (PARI) vector(66,n,sigma(2*n,1))
%o (PARI) for (n=1, 1000, write("b062731.txt", n, " ", sigma(2*n)) ) \\ _Harry J. Smith_, Aug 09 2009
%o (MuPAD) numlib::sigma(2*n)$ n=0..81 // _Zerinvary Lajos_, May 13 2008
%o (Magma) [SumOfDivisors(2*n): n in [1..70]]; // _Vincenzo Librandi_, Oct 31 2014
%Y Sigma(k*n): A000203 (k=1), A144613 (k=3), A193553 (k=4, even bisection), A283118 (k=5), A224613 (k=6), A283078 (k=7), A283122 (k=8), A283123 (k=9).
%Y Cf. A008438, A074400, A182818, A239052 (odd bisection), A326124 (partial sums), A054784, A215947, A336923, A346870, A346878, A346880, A355750.
%Y Row 2 of A319526. Column & Row 2 of A216626. Row 1 of A355927.
%Y Shallow diagonal (2n,n) of A265652. See also A244658.
%K easy,nonn
%O 1,1
%A _Jason Earls_, Jul 11 2001
%E Zero removed and offset corrected by _Omar E. Pol_, Jul 17 2009
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