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 A110928 #13 Sep 08 2019 04:34:27
%S A110928 6,7,24,26,30,35,40,47,66,77,78,91,102,119,114,133,120,130,120,141,
%T A110928 130,141,136,157,138,161,150,175,168,182,174,203,186,215,186,217,215,
%U A110928 217,222,259,230,249,246,287,258,301,264,286,280,282,280,329,282,329,318
%N A110928 Pairs of distinct numbers m and n, m<n, such that sigma_2(m)=sigma_2(n), where sigma_2(n) is the sum of the squares of all divisors of n.
%C A110928 There do not appear to be any pairs (m,n) such that sigma_k(m)=sigma_k(n) for k>2.
%C A110928 For sigma_3, the first pair is (184926, 194315). Other terms may be found in A131907 and A131908. See A158915.
%H A110928 Amiram Eldar, <a href="/A110928/b110928.txt">Table of n, a(n) for n = 1..10000</a>
%F A110928 sigma_2(m)=sigma_2(n), m<n.
%e A110928 sigma_2(30)=1^1+2^2+3^2+5^2+6^2+10^2+15^2+30^2=1300 and sigma_2(35)=1^2+5^2+7^2+35^2=1300.
%p A110928 with(numtheory); sigmap := proc(p,n) convert(map(proc(z) z^p end, divisors(n)),`+`) end; SA2:=[]: for z from 1 to 1 do for m to 1500 do M:=sigmap(2,m); for n from m+1 to 1500 do N:=sigmap(2,n); if N=M then SA2:=[op(SA2),[m,n,N]] fi od od od; SA2; select(proc(z) z[1]<=1000 end, SA2); #just to shorten it a bit
%t A110928 a[n_] := Module[{s = DivisorSigma[2, n], ans = {}}, kmax = Ceiling[Sqrt[s]]; Do[If[DivisorSigma[2, k] == s, AppendTo[ans, k]], {k, n + 1, kmax}]; ans]; s = {}; Do[v = a[n]; Do[s = Join[s, {n, v[[k]]}], {k, 1, Length[v]}], {n, 1, 400}]; s (* _Amiram Eldar_, Sep 08 2019 *)
%Y A110928 Cf. A001157, A002025, A002046, A063990.
%Y A110928 Cf. A110926, A110927, A110929.
%K A110928 nonn,tabf
%O A110928 1,1
%A A110928 _Walter Kehowski_, Sep 23 2005