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%I #21 Feb 21 2015 09:22:15
%S 0,0,0,1,2,2,3,4,4,5,6,7,7,8,9,9,10,11,12,12,13,14,15,15,16,17,18,18,
%T 19,20,21,21,22,23,24,25,25,26,27,28,28,29,30,31,32,32,33,34,35,35,36,
%U 37,38,39,39,40,41,42,42,43,44,45,46,46,47,48,49,50,50,51,52
%N a(n) = j such that i^j is maximized subject to i+j = n (i >= 0, j >= 0).
%C For n = 2, there is not a unique maximum because 2^0 = 1^1; we choose j = 0. - _T. D. Noe_, Apr 08 2014
%H T. D. Noe, <a href="/A125229/b125229.txt">Table of n, a(n) for n = 0..1000</a>
%e If the sum is 5, the powers are: 0^5, 1^4, 2^3, 3^2, 4^1 and 5^0. The highest is 3^2 so a(5) = 2.
%t Join[{0,0},Table[SortBy[{#[[1]],#[[2]],#[[1]]^#[[2]]}&/@Flatten[ Permutations /@ IntegerPartitions[n,{2}],1],Last][[-1,2]],{n,3,80}]] (* _Harvey P. Dale_, Sep 01 2013 *)
%t Join[{0, 0, 0}, Flatten[Table[s = Table[(n - k)^k, {k, n}]; Position[s, Max[s]], {n, 3, 80}]]] (* _T. D. Noe_, Apr 08 2014 *)
%Y Cf. A056155.
%K easy,nonn
%O 0,5
%A _Sébastien Dumortier_, Jan 15 2007
%E a(0) added by _T. D. Noe_, Apr 08 2014
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