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A239052
Sum of divisors of 4*n-2.
8
3, 12, 18, 24, 39, 36, 42, 72, 54, 60, 96, 72, 93, 120, 90, 96, 144, 144, 114, 168, 126, 132, 234, 144, 171, 216, 162, 216, 240, 180, 186, 312, 252, 204, 288, 216, 222, 372, 288, 240, 363, 252, 324, 360, 270, 336, 384, 360, 294, 468, 306, 312, 576
OFFSET
1,1
COMMENTS
Bisection of A062731 (odd part).
a(n) is also the total number of cells in the n-th branch of the second quadrant of the spiral formed by the parts of the symmetric representation of sigma(4n-2). For the quadrants 1, 3, 4 see A112610, A239053, A193553. The spiral has been obtained according to the following way: A196020 --> A236104 --> A235791 --> A237591 --> A237593 --> A237270, see example.
We can find the spiral on the terraces of the stepped pyramid described in A244050. - Omar E. Pol, Dec 07 2016
LINKS
FORMULA
a(n) = A000203(4n-2) = A000203(A016825(n-1)).
a(n) = 3*A008438(n-1). - Joerg Arndt, Mar 09 2014
Sum_{k=1..n} a(k) = (3*Pi^2/8) * n^2 + O(n*log(n)). - Amiram Eldar, Dec 17 2022
EXAMPLE
Illustration of initial terms:
------------------------------------------------------
. Branches of the spiral
. in the second quadrant n a(n)
------------------------------------------------------
.
. _ _ _ _ _ _ _ _
. | _ _ _ _ _ _ _| 4 24
. | |
. 12 _| |
. |_ _| _ _ _ _ _ _
. 12 _ _| | _ _ _ _ _| 3 18
. _ _ _| | 9 _| |
. | _ _ _| 9 _|_ _|
. | | _ _| | _ _ _ _
. | | | _ _| 12 _| _ _ _| 2 12
. | | | | _| |
. | | | | | _ _|
. | | | | | | 3 _ _
. | | | | | | | _| 1 3
. |_| |_| |_| |_|
.
For n = 4 the sum of divisors of 4*n-2 is 1 + 2 + 7 + 14 = A000203(14) = 24. On the other hand the parts of the symmetric representation of sigma(14) are [12, 12] and the sum of them is 12 + 12 = 24, equaling the sum of divisors of 14, so a(4) = 24.
MATHEMATICA
a[n_] := DivisorSigma[1, 4*n - 2]; Array[a, 100] (* Amiram Eldar, Dec 17 2022 *)
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Mar 09 2014
STATUS
approved