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A241838 Column 1 of A237270, also the right border.

%I A241838 #25 Aug 08 2018 05:42:49
%S A241838 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 A241838 56,15,72,16,63,17,27,18,91,19,30,20,90,21,96,22,42,23,36,24,124,25,
%U A241838 39,26,49,27,120,28,120,29,45,30,168,31,48,32,127
%N A241838 Column 1 of A237270, also the right border.
%C A241838 First differs from A241559 at a(45).
%C A241838 If A237271(n) = 1 then a(n) = A241558(n) = A241559(n) = A000203(n).
%C A241838 If n is an odd prime then a(n) = (n + 1)/2 = A241558(n) = A241559(n).
%C A241838 For more information see A237593.
%H A241838 Robert Price, <a href="/A241838/b241838.txt">Table of n, a(n) for n = 1..10000</a>
%F A241838 a(n) = A237270(n, 1) = A237270(n, A237271(n)).
%e A241838 For n = 45 the symmetric representation of sigma(45) = 78 has three parts [23, 32, 23], both the first and the last term are equal to 23, so a(45) = 23.
%t A241838 Map[First[a237270[#]]&,Range[64]] (* data : computing all parts *)
%t A241838 (* computing only the first part of the symmetric representation of sigma(n) *)
%t A241838 row[n_] := Floor[(Sqrt[8n+1]-1)/2] (* in A237591 *)
%t A241838 f[n_, k_] := If[Mod[n-k*(k+1)/2, k]==0, (-1)^(k+1), 0]
%t A241838 g[n_, k_] := Ceiling[(n+1)/k-(k+1)/2] - Ceiling[(n+1)/(k+1)-(k+2)/2] (* in A237591 *)
%t A241838 a241838[n_] := Module[{r=row[n], widths={}, i=1, w=0, len, legs}, w+=f[n, i]; While[i<=r && w!=0, AppendTo[widths, w]; i++; w+=f[n, i]]; len=Length[widths]; legs=Map[g[n, #]&, Range[len]]; If[len<r, widths.legs, 2*widths.legs-Last[widths]]]
%t A241838 Map[a241838,Range[64]] (* data *)
%t A241838 (* _Hartmut F. W. Hoft_, Jan 25 2018 *)
%Y A241838 Cf. A000203, A071561, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A241558, A241559, A245092, A262626.
%K A241838 nonn,look
%O A241838 1,2
%A A241838 _Omar E. Pol_, Apr 29 2014