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 A337360 #18 Aug 31 2025 16:29:47
%S A337360 2,9,12,28,18,60,24,75,52,90,36,196,42,120,120,186,54,273,60,294,160,
%T A337360 180,72,540,124,210,200,392,90,648,96,441,240,270,240,910,114,300,280,
%U A337360 810,126,864,132,588,546,360,144,1364,228,651,360,686,162,1080,360,1080,400,450,180,2184
%N A337360 a(n) = sigma(n) * (tau(n) + 1).
%C A337360 Original name was: Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 <= d2.
%C A337360 2*a(n) is the sum of the perimeters of all distinct rectangles that can be made whose side lengths are divisors of n.
%C A337360 Every divisor of n occurs tau(n) + 1 times in the coordinates of divisors of n. - _David A. Corneth_, Aug 25 2020
%H A337360 David A. Corneth, <a href="/A337360/b337360.txt">Table of n, a(n) for n = 1..10000</a>
%F A337360 a(n) = Sum_{d1|n, d2|n, d1<=d2} (d1+d2).
%F A337360 a(p^k) = (p^(k+1)-1)*(k+2)/(p-1) for p prime and k >= 1. - _Wesley Ivan Hurt_, Aug 23 2025
%e A337360 a(3) = 12; The divisors of 3 are {1,3}. The divisor pairs, (d1,d2), where d1 <= d2 are (1,1), (1,3) and (3,3). The sum of all the coordinates is then 1+1+1+3+3+3 = 12. So a(3) = 12.
%e A337360 a(4) = 28; The divisors of 4 are {1,2,4}. The divisor pairs, (d1,d2), where d1 <= d2 are (1,1), (1,2), (1,4), (2,2), (2,4) and (4,4). The sum of all the coordinates is then 1+1+1+2+1+4+2+2+2+4+4+4 = 28. So a(4) = 28.
%e A337360 a(5) = 18; The divisors of 5 are {1,5}. The divisor pairs, (d1,d2), where d1 <= d2 are (1,1), (1,5) and (5,5). The sum of all the coordinates is then 1+1+1+5+5+5 = 18. So a(5) = 18.
%e A337360 a(6) = 60; The divisors of 6 are {1,2,3,6}. The divisor pairs, (d1,d2), where d1 <= d2 are (1,1), (1,2), (1,3), (1,6), (2,2), (2,3), (2,6), (3,3), (3,6), (6,6). The sum of all the coordinates is then 1+1+1+2+1+3+1+6+2+2+2+3+2+6+3+3+3+6+6+6 = 60. So a(6) = 60.
%t A337360 Table[Sum[Sum[(i + k) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k}], {k, n}], {n, 80}]
%o A337360 (PARI) a(n) = sigma(n) * (numdiv(n)+1) \\ _David A. Corneth_, Aug 25 2020
%o A337360 (Python)
%o A337360 from sympy import divisor_sigma
%o A337360 def A337360(n): return (divisor_sigma(n,0)+1)*divisor_sigma(n) # _Chai Wah Wu_, Aug 07 2025
%Y A337360 Cf. A000005 (tau), A000203 (sigma).
%K A337360 nonn,easy,changed
%O A337360 1,1
%A A337360 _Wesley Ivan Hurt_, Aug 24 2020
%E A337360 New name using formula from David A. Corneth_, Aug 25 2020