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A347980 a(n) is the smallest odd number k whose symmetric representation of sigma(k) has maximum width n.

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%I A347980 #17 Sep 23 2021 12:04:36
%S A347980 1,15,315,2145,3465,17325,45045,51975,225225,405405,315315,765765,
%T A347980 1576575,2297295
%N A347980 a(n) is the smallest odd number k whose symmetric representation of sigma(k) has maximum width n.
%C A347980 The sequence is not increasing with the maximum width of the symmetric representation just like A347979.
%C A347980 Observation: a(2)..a(14) ending in 5. - _Omar E. Pol_, Sep 23 2021
%e A347980 The pattern of maximum widths of the parts in the symmetric representation of sigma for the first four terms in the sequence is:
%e A347980    a(n) parts  successive widths
%e A347980      1:   1          1
%e A347980     15:   3        1 2 1
%e A347980    315:   3        1 3 1
%e A347980   2145:   7    1 2 3 4 3 2 1
%t A347980 a262045[n_] := Module[{a=Accumulate[Map[If[Mod[n - # (#+1)/2, #]==0, (-1)^(#+1), 0] &, Range[Floor[(Sqrt[8n+1]-1)/2]]]]}, Join[a, Reverse[a]]]
%t A347980 a347980[n_, mw_] := Module[{list=Table[0, mw], i, v}, For[i=1, i<=n, i+=2, v=Max[a262045[i]]; If [list[[v]]==0, list[[v]]=i]]; list]
%t A347980 a347980[2500000,14] (* long evaluation time *)
%Y A347980 Cf. A174973, A237048, A237270, A237271, A237591, A237593, A238443, A249351 (widths), A250070, A262045, A341969, A341970, A341971, A347979.
%K A347980 nonn,more
%O A347980 1,2
%A A347980 _Hartmut F. W. Hoft_, Sep 22 2021