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 A175705 #15 Aug 20 2025 08:27:50
%S A175705 1,10,45,142,362,780,1561,2762,4808,7570,12034,17482,26072,35884,
%T A175705 50909,67012,92111,116950,155720,193564,250914,304244,389286,461654,
%U A175705 578952,680944,839304,970094,1188924,1354164,1637145,1858344,2215866,2485068
%N A175705 Convolution square of A001157 (the sum of squared divisors).
%H A175705 Amiram Eldar, <a href="/A175705/b175705.txt">Table of n, a(n) for n = 1..10000</a>
%F A175705 a(n) = Sum_{k=1..n} A001157(k)* A001157(n+1-k).
%F A175705 G.f.: (1/x)*(Sum_{k>=1} k^2*x^k/(1 - x^k))^2. - _Ilya Gutkovskiy_, Jan 01 2017
%F A175705 Conjecture: Sum_{k=1..n} a(k) ~ zeta(3)^2 * n^6 / 180. - _Vaclav Kotesovec_, Aug 20 2025
%p A175705 with(numtheory): T:=array(1..200):for p from 1 to 200 do: liste:=divisors(p) :s2:=sum(liste[i]^2,i=1..nops(liste)):T[p] :=s2 :od : for n from 1 to 100 do: printf(`%d, `, sum (T[k]*T[n+1-k],k=1..n)):od:
%t A175705 a[n_] := Sum[DivisorSigma[2, k] * DivisorSigma[2, n + 1 - k], {k, 1, n}]; Array[a, 34] (* _Amiram Eldar_, Jul 31 2019 *)
%Y A175705 Cf. A001157, A328490.
%K A175705 nonn
%O A175705 1,2
%A A175705 _Michel Lagneau_, Aug 10 2010
%E A175705 Definition slightly rephrased by _R. J. Mathar_, Aug 19 2010