This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A239052 #28 Dec 17 2022 04:23:26
%S A239052 3,12,18,24,39,36,42,72,54,60,96,72,93,120,90,96,144,144,114,168,126,
%T A239052 132,234,144,171,216,162,216,240,180,186,312,252,204,288,216,222,372,
%U A239052 288,240,363,252,324,360,270,336,384,360,294,468,306,312,576
%N A239052 Sum of divisors of 4*n-2.
%C A239052 Bisection of A062731 (odd part).
%C A239052 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.
%C A239052 We can find the spiral on the terraces of the stepped pyramid described in A244050. - Omar E. Pol, Dec 07 2016
%H A239052 Amiram Eldar, <a href="/A239052/b239052.txt">Table of n, a(n) for n = 1..10000</a>
%F A239052 a(n) = A000203(4n-2) = A000203(A016825(n-1)).
%F A239052 a(n) = 3*A008438(n-1). - _Joerg Arndt_, Mar 09 2014
%F A239052 Sum_{k=1..n} a(k) = (3*Pi^2/8) * n^2 + O(n*log(n)). - _Amiram Eldar_, Dec 17 2022
%e A239052 Illustration of initial terms:
%e A239052 ------------------------------------------------------
%e A239052 . Branches of the spiral
%e A239052 . in the second quadrant n a(n)
%e A239052 ------------------------------------------------------
%e A239052 .
%e A239052 . _ _ _ _ _ _ _ _
%e A239052 . | _ _ _ _ _ _ _| 4 24
%e A239052 . | |
%e A239052 . 12 _| |
%e A239052 . |_ _| _ _ _ _ _ _
%e A239052 . 12 _ _| | _ _ _ _ _| 3 18
%e A239052 . _ _ _| | 9 _| |
%e A239052 . | _ _ _| 9 _|_ _|
%e A239052 . | | _ _| | _ _ _ _
%e A239052 . | | | _ _| 12 _| _ _ _| 2 12
%e A239052 . | | | | _| |
%e A239052 . | | | | | _ _|
%e A239052 . | | | | | | 3 _ _
%e A239052 . | | | | | | | _| 1 3
%e A239052 . |_| |_| |_| |_|
%e A239052 .
%e A239052 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.
%t A239052 a[n_] := DivisorSigma[1, 4*n - 2]; Array[a, 100] (* _Amiram Eldar_, Dec 17 2022 *)
%Y A239052 Cf. A000203, A008438, A016825, A062731, A074400, A112610, A193553, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239050, A239053, A244050, A245092, A262626.
%K A239052 nonn,easy
%O A239052 1,1
%A A239052 _Omar E. Pol_, Mar 09 2014