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 A081307 #30 Jul 09 2025 15:08:08
%S A081307 1,3,4,8,6,16,8,21,17,26,12,50,14,36,40,54,18,75,20,84,56,56,24,140,
%T A081307 47,66,72,118,30,176,32,135,88,86,96,242,38,96,104,238,42,248,44,186,
%U A081307 198,116,48,366,93,213,136,220
%N A081307 a(n) = (n+1)*tau(n) - sigma(n).
%C A081307 Old name was: Sum_{k=1..n} Sum_{m=1..k} 1/(1-x^m).
%C A081307 Number of positive integer pairs (s,t) with s <= t <= n, such that s|n. For example, when n = 6, the 16 pairs are (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (6,6). - _Wesley Ivan Hurt_, Nov 15 2021
%H A081307 Hugo Pfoertner, <a href="/A081307/b081307.txt">Table of n, a(n) for n = 1..10000</a>
%F A081307 Sum_{k=1..n} Sum_{m=1..k} 1/(1-x^m).
%F A081307 a(n) = Sum_{k=1..n} k*A113998(n,k). - _Philippe Deléham_, Feb 03 2007
%t A081307 Table[(n + 1) DivisorSigma[0, n] - DivisorSigma[1, n], {n, 100}] (* _Wesley Ivan Hurt_, Nov 15 2021 *)
%o A081307 (PARI) a(n)=if(n<1,0,polcoeff(sum(k=1,n,sum(l=1,k,1/(1-x^l)),x*O(x^n)),n))
%o A081307 (PARI) a(n)=sum(j=1, n, sum(k=1, j, n%k==0)) \\ _Hugo Pfoertner_, Jul 09 2025
%Y A081307 Cf. A000005 (tau), A000203 (sigma), A094471, A113998.
%K A081307 nonn
%O A081307 1,2
%A A081307 _Benoit Cloitre_, Apr 20 2003
%E A081307 Name changed by _Wesley Ivan Hurt_, Nov 16 2021 using formula from _Vladeta Jovovic_, Jan 22 2005