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A110929 The common value of sigma_2 for square-amicable numbers, sigma_2(m)=sigma_2(n), m

%I A110929 #10 Sep 08 2019 04:34:21
%S A110929 50,850,1300,2210,6100,8500,14500,18100,22100,22100,22100,24650,26500,
%T A110929 32550,42500,42100,48100,48100,48100,68500,68900,84100,92500,103700,
%U A110929 110500,110500,110500,140500,158600,174100,201110,186100,221000,224500
%N A110929 The common value of sigma_2 for square-amicable numbers, sigma_2(m)=sigma_2(n), m<n.
%H A110929 Amiram Eldar, <a href="/A110929/b110929.txt">Table of n, a(n) for n = 1..10000</a>
%F A110929 sigma_2(m)=sigma_2(n), m<n.
%e A110929 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 A110929 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 A110929 a[n_] := Module[{s = DivisorSigma[2, n], ans = {}}, kmax = Ceiling[Sqrt[s]]; Do[If[DivisorSigma[2, k] == s, AppendTo[ans, s]], {k, n + 1, kmax}]; ans];  s = {}; Do[v = a[n]; Do[AppendTo[s,  v[[k]]], {k, 1, Length[v]}], {n, 1, 400}]; s (* _Amiram Eldar_, Sep 08 2019 *)
%Y A110929 Cf. A001157, A002025, A002046, A063990.
%Y A110929 Cf. A110926, A110927, A110928.
%K A110929 nonn
%O A110929 1,1
%A A110929 _Walter Kehowski_, Sep 23 2005