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 A337297 #19 Aug 23 2025 20:47:36
%S A337297 0,3,4,14,6,36,8,45,26,54,12,140,14,72,72,124,18,195,20,210,96,108,24,
%T A337297 420,62,126,120,280,30,504,32,315,144,162,144,728,38,180,168,630,42,
%U A337297 672,44,420,390,216,48,1116,114,465,216,490,54,840,216,840,240,270,60,1848,62,288
%N A337297 a(n) = sigma(n)*(tau(n) - 1).
%C A337297 Original name was: Sum of the coordinates of all pairs of divisors of n, (d1,d2), such that d1 < d2.
%C A337297 If n = p where p is prime, the only pair of divisors of p such that d1 < d2 is (1,p), whose coordinate sum is a(p) = p + 1. - _Wesley Ivan Hurt_, May 21 2021
%F A337297 a(n) = Sum_{d1|n, d2|n, d1<d2} (d1 + d2).
%F A337297 a(p^k) = k*(p^(k+1)-1)/(p-1) for p prime and k >= 1. - _Wesley Ivan Hurt_, Aug 23 2025
%e A337297 a(3) = 4; The divisors of 3 are {1,3}. If we form all ordered pairs (d1,d2) such that d1 < d2, we have: (1,3). The sum of the coordinates gives 1+3 = 4.
%e A337297 a(4) = 14; The divisors of 4 are {1,2,4}. If we form all ordered pairs (d1,d2) such that d1<d2, we have: (1,2), (1,4), (2,4). The sum of all the coordinates gives 1+2+1+4+2+4 = 14.
%t A337297 Table[Sum[Sum[(i + k)*(1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, n}], {n, 100}]
%o A337297 (PARI) a(n) = my(d = divisors(n)); sum(i=1, #d, sum(j=1, i-1, d[i]+d[j])); \\ _Michel Marcus_, Aug 22 2020
%Y A337297 Cf. A066446, A184389, A337246.
%Y A337297 Cf. A000005, A000203, A337360.
%K A337297 nonn,easy,changed
%O A337297 1,2
%A A337297 _Wesley Ivan Hurt_, Aug 21 2020
%E A337297 New name using formula from _Ridouane Oudra_, Jul 31 2025