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A241559 Largest part of the symmetric representation of sigma(n).

%I A241559 #22 Jan 06 2017 08:21:13
%S A241559 1,3,2,7,3,12,4,15,5,9,6,28,7,12,8,31,9,39,10,42,11,18,12,60,13,21,14,
%T A241559 56,15,72,16,63,17,27,18,91,19,30,20,90,21,96,22,42,32,36,24,124,25,
%U A241559 39,26,49,27,120,28,120,29,45,30,168,31,48,32,127
%N A241559 Largest part of the symmetric representation of sigma(n).
%C A241559 First differs from A241838 at a(45).
%C A241559 If A237271(n) = 1 then a(n) = A241558(n) = A241838(n) = A000203(n).
%C A241559 If n is an odd prime then a(n) = (n + 1)/2 = A241558(n) = A241838(n).
%C A241559 For more information see A237593.
%e A241559 For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
%e A241559 y
%e A241559 .
%e A241559 ._ _ _ _ _ 5
%e A241559 |_ _ _ _ _|
%e A241559 .         |_ _ 3
%e A241559 .         |_  |
%e A241559 .           |_|_ _ 5
%e A241559 .               | |
%e A241559 .               | |
%e A241559 .               | |
%e A241559 .               | |
%e A241559 . . . . . . . . |_| . . x
%e A241559 .
%e A241559 There are three parts [5, 3, 5] and the largest part is 5 so a(9) = 5.
%e A241559 For n = 45 the symmetric representation of sigma(45) = 78 has three parts [23, 32, 23] and the largest part is 32 so a(45) = 32.
%t A241559 (* Function a237270[] is defined in A237270 *)
%t A241559 a241559[n_]:=Max[a237270[n]]
%t A241559 Map[a241559,Range[64]] (* data *)
%t A241559 (* _Hartmut F. W. Hoft_, Sep 19 2014 *)
%Y A241559 Cf. A000203, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A241558, A071561, A071562, A241838.
%K A241559 nonn
%O A241559 1,2
%A A241559 _Michel Marcus_ and _Omar E. Pol_, Apr 29 2014