A265652 -id:A265652 - cp's OEIS frontend

A062731 Sum of divisors of 2*n.

3, 7, 12, 15, 18, 28, 24, 31, 39, 42, 36, 60, 42, 56, 72, 63, 54, 91, 60, 90, 96, 84, 72, 124, 93, 98, 120, 120, 90, 168, 96, 127, 144, 126, 144, 195, 114, 140, 168, 186, 126, 224, 132, 180, 234, 168, 144, 252, 171, 217, 216, 210, 162, 280, 216, 248, 240, 210

Offset: 1

Jason Earls, Jul 11 2001

a(n) is also the total number of parts in all partitions of 2*n into equal parts. - Omar E. Pol, Feb 14 2021

N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [First 1000 terms from Harry J. Smith]

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).
Cf. A008438, A074400, A182818, A239052 (odd bisection), A326124 (partial sums), A054784, A215947, A336923, A346870, A346878, A346880, A355750.
Row 2 of A319526. Column & Row 2 of A216626. Row 1 of A355927.
Shallow diagonal (2n,n) of A265652. See also A244658.

[SumOfDivisors(2*n): n in [1..70]]; // Vincenzo Librandi, Oct 31 2014

lst={};Do[AppendTo[lst, DivisorSigma[1, n]], {n, 2, 6!, 2}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 20 2008 *)
DivisorSigma[1,2*Range[60]] (* Harvey P. Dale, Jun 08 2022 *)

numlib::sigma(2*n)$ n=0..81 // Zerinvary Lajos, May 13 2008

PARI
```
vector(66,n,sigma(2*n,1))
```

for (n=1, 1000, write("b062731.txt", n, " ", sigma(2*n)) ) \\ Harry J. Smith, Aug 09 2009

a(n) = A000203(2*n). - R. J. Mathar, Apr 06 2011
a(n) = A000203(n) + A054785(n). - R. J. Mathar, May 19 2020
From Vaclav Kotesovec, Aug 07 2022: (Start)
Dirichlet g.f.: zeta(s) * zeta(s-1) * (3 - 2^(1-s)).
Sum_{k=1..n} a(k) ~ 5 * Pi^2 * n^2 / 24. (End)
From Miles Wilson, Sep 30 2024: (Start)
G.f.: Sum_{k>=1} k*x^(k/gcd(k, 2))/(1 - x^(k/gcd(k, 2))).
G.f.: Sum_{k>=1} k*x^(2*k/(3 + (-1)^k))/(1 - x^(2*k/(3 + (-1)^k))). (End)

Zero removed and offset corrected by Omar E. Pol, Jul 17 2009

A245093 Triangle read by rows in which row n lists the first n terms of A000203.

Original entry on oeis.org

1, 1, 3, 1, 3, 4, 1, 3, 4, 7, 1, 3, 4, 7, 6, 1, 3, 4, 7, 6, 12, 1, 3, 4, 7, 6, 12, 8, 1, 3, 4, 7, 6, 12, 8, 15, 1, 3, 4, 7, 6, 12, 8, 15, 13, 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28

Offset: 1

Omar E. Pol, Jul 15 2014

Reluctant sequence of A000203.
Row sums give A024916.
Has a symmetric representation - for more information see A237270.

			Triangle begins:
1;
1, 3;
1, 3, 4;
1, 3, 4, 7;
1, 3, 4, 7, 6;
1, 3, 4, 7, 6, 12;
1, 3, 4, 7, 6, 12, 8;
1, 3, 4, 7, 6, 12, 8, 15;
1, 3, 4, 7, 6, 12, 8, 15, 13;
1, 3, 4, 7, 6, 12, 8, 15, 13, 18;
1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12;
1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28;

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Cf. A000203, A024916, A027293, A104765, A140207, A221529, A237270, A237593, A245099, A265652.

import Data.List (inits)
a245093 n k = a245093_tabl !! (n-1) !! (k-1)
a245093_row n = a245093_tabl !! (n-1)
a245093_tabl = tail $ inits $ a000203_list
-- Reinhard Zumkeller, Dec 12 2015

T(n,k) = A000203(k), 1<=k<=n.

cp's OEIS Frontend

A062731 Sum of divisors of 2*n.

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