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%I #26 Nov 06 2024 04:39:03
%S 1,3,0,7,0,12,0,15,3,0,0,28,0,0,8,31,0,39,0,42,0,0,0,60,5,0,0,56,0,72,
%T 0,63,0,0,12,91,0,0,0,90,0,96,0,0,32,0,0,124,7,15,0,0,0,120,0,120,0,0,
%U 0,168,0,0,16,127,0,144,0,0,0,36,0,195,0,0,0,0,18,0,0,186,9,0,0,224,0
%N a(n) is the size of the central part of the symmetric representation of sigma(n), or 0 if such a part does not exits.
%C a(n) = A000203(n) if and only if n is a member of A174973.
%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 central part is 3 so a(9) = 3.
%Y Indices of odd terms give A028982.
%Y Indices of even terms give A028983.
%Y Indices of zeros give A071561.
%Y Indices of nonzero terms give A071562.
%Y Nonzero terms give A295423.
%Y Parity gives A053866.
%Y Has the same parity as A000203, A000593, A001227, A033879, A033880, A067742.
%Y Cf. A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A241558, A241559, A245092, A262626, A347950.
%K nonn
%O 1,2
%A _Omar E. Pol_, Oct 29 2024