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