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A211217 Maximum of sigma(x) * sigma(y), where x + y = n.

%I A211217 #18 Aug 11 2014 22:45:48
%S A211217 1,3,9,12,21,28,49,48,84,72,144,96,180,156,225,195,336,234,420,364,
%T A211217 504,360,784,432,672,672,868,576,1092,744,1176,936,1209,1008,1680,992,
%U A211217 1638,1440,1860,1344,2340,1344,2520,1920,2232,1680,3600,1860,3024,2400
%N A211217 Maximum of sigma(x) * sigma(y), where x + y = n.
%H A211217 Paolo P. Lava, <a href="/A211217/b211217.txt">Table of n, a(n) for n = 2..10000</a>
%H A211217 Paolo P. Lava, <a href="/A211217/a211217.pdf">Plot of the first 10000 terms of the sequence</a>
%e A211217 For n=83 the maximum product is reached when 35 and 48 (35+48=83) are considered: sigma(35)*sigma(48) = 48*124 = 5952.
%e A211217 For n=99 the maximum product is reached when 36 and 63 (36+63=99) are considered: sigma(36)*sigma(63) = 91*104 = 9464.
%p A211217 with(combstruct); with(numtheory);
%p A211217 A211217:=proc(i)
%p A211217 local a,b,j,n,t;
%p A211217 for n from 2 to i do
%p A211217   t:=0;
%p A211217   for j from 0 to floor(n/2) do
%p A211217     a:=n-j; b:=sigma(j)*sigma(a); if b>t then t:=b; fi;
%p A211217   od;
%p A211217   print(t);
%p A211217 od; end:
%p A211217 A211217(1000);
%t A211217 a[n_] := Max[Times @@ DivisorSigma[1, #]& /@ IntegerPartitions[n, {2}]]; Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, Dec 26 2013 *)
%Y A211217 Cf. A211216, A211218, A211219.
%K A211217 nonn
%O A211217 2,2
%A A211217 _Paolo P. Lava_, Apr 05 2012