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A211218 Maximum value of sigma(x) + sigma(y) + sigma(z), where x + y + z = n.

%I A211218 #22 Dec 26 2013 08:45:49
%S A211218 3,5,7,9,11,14,16,18,20,22,25,30,32,34,36,38,41,43,44,47,47,52,57,62,
%T A211218 64,66,68,70,73,75,76,79,80,84,89,93,95,97,99,101,104,106,107,110,110,
%U A211218 116,121,126,128,130,132,134,137,139,140,143
%N A211218 Maximum value of sigma(x) + sigma(y) + sigma(z), where x + y + z = n.
%C A211218 Not monotonic: a(86) = 235 > 234 = a(87). - _Charles R Greathouse IV_, Apr 06 2012
%H A211218 Charles R Greathouse IV, <a href="/A211218/b211218.txt">Table of n, a(n) for n = 3..10000</a>
%e A211218 a(76) = sigma(4)+sigma(12)+sigma(60) = 7 + 28 + 168 = 203.
%e A211218 a(83) = sigma(1)+sigma(10)+sigma(72) = 1 + 18 + 195 = 214.
%p A211218 with(numtheory) :
%p A211218 A211218 := proc(n)
%p A211218         local x,y,z,mx ;
%p A211218         mx := 0 ;
%p A211218         for x from 1 to n do
%p A211218                 for y from x do
%p A211218                         z := n-x-y ;
%p A211218                         if z < y then
%p A211218                                 break;
%p A211218                         end if;
%p A211218                         mx := max(mx, sigma(x)+sigma(y)+sigma(z)) ;
%p A211218                 end do:
%p A211218         end do:
%p A211218         mx ;
%p A211218 end proc: # _R. J. Mathar_, Apr 05 2012
%t A211218 a[n_] := Max[Plus @@ DivisorSigma[1, #]& /@ IntegerPartitions[n, {3}]]; Table[a[n], {n, 3, 100}] (* _Jean-François Alcover_, Dec 26 2013 *)
%o A211218 (PARI) v=vector(200);for(n=2,#v,best=sigma(n-1)+1;for(k=2,n\2, best=max(best,sigma(k)+sigma(n-k)));v[n]=best)
%o A211218 u=vector(#v);for(n=3,#u,best=sigma(n-2)+v[2];for(k=2,n-3, best=max(best,sigma(k)+v[n-k]));u[n]=best)
%o A211218 vecextract(u,"3..") \\ _Charles R Greathouse IV_, Apr 06 2012
%Y A211218 Cf. A085884, A211217, A211219.
%K A211218 nonn
%O A211218 3,1
%A A211218 _Paolo P. Lava_, Apr 05 2012
%E A211218 Rewritten by R. J. Mathar, Apr 05 2012