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A241558 Smallest part of the symmetric representation of sigma(n).

%I A241558 #24 Feb 14 2020 09:27:02
%S A241558 1,3,2,7,3,12,4,15,3,9,6,28,7,12,8,31,9,39,10,42,5,18,12,60,5,21,6,56,
%T A241558 15,72,16,63,7,27,12,91,19,30,8,90,21,96,22,42,23,36,24,124,7,15,10,
%U A241558 49,27,120,8,120,11,45,30,168,31,48,12,127,9,144,34,63,13
%N A241558 Smallest part of the symmetric representation of sigma(n).
%C A241558 If A237271(n) = 1 then a(n) = A241559(n) = A241838(n) = A000203(n).
%C A241558 If n is an odd prime then a(n) = (n + 1)/2 = A241559(n) = A241838(n).
%C A241558 For more information see A237270 and A237593.
%H A241558 Jinyuan Wang, <a href="/A241558/b241558.txt">Table of n, a(n) for n = 1..1000</a>
%e A241558 For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
%e A241558 y
%e A241558 .
%e A241558 ._ _ _ _ _ 5
%e A241558 |_ _ _ _ _|
%e A241558 .         |_ _ 3
%e A241558 .         |_  |
%e A241558 .           |_|_ _ 5
%e A241558 .               | |
%e A241558 .               | |
%e A241558 .               | |
%e A241558 .               | |
%e A241558 . . . . . . . . |_| . . x
%e A241558 .
%e A241558 There are three parts [5, 3, 5] and the smallest part is 3 so a(9) = 3.
%e A241558 For n = 45 the symmetric representation of sigma(45) = 78 has three parts [23, 32, 23] and the smallest part is 23 so a(45) = 23.
%e A241558 For n = 63 the symmetric representation of sigma(63) = 104 has five parts [32, 12, 16, 12, 32] and the smallest part is 12 so a(63) = 12.
%t A241558 (* Function a237270[] is defined in A237270 *)
%t A241558 a241558[n_]:=Min[a237270[n]]
%t A241558 Map[a241558,Range[64]] (* data *)
%t A241558 (* _Hartmut F. W. Hoft_, Sep 19 2014 *)
%Y A241558 Cf. A000203, A071561, A071562, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A241559, A241838, A245092, A262626.
%K A241558 nonn
%O A241558 1,2
%A A241558 _Michel Marcus_ and _Omar E. Pol_, Apr 29 2014
%E A241558 More terms from _Jinyuan Wang_, Feb 14 2020