A347980 - OEIS

%I #17 Sep 23 2021 12:04:36

%S 1,15,315,2145,3465,17325,45045,51975,225225,405405,315315,765765,

%T 1576575,2297295

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

%C The sequence is not increasing with the maximum width of the symmetric representation just like A347979.

%C Observation: a(2)..a(14) ending in 5. - _Omar E. Pol_, Sep 23 2021

%e The pattern of maximum widths of the parts in the symmetric representation of sigma for the first four terms in the sequence is:

%e    a(n) parts  successive widths

%e      1:   1          1

%e     15:   3        1 2 1

%e    315:   3        1 3 1

%e   2145:   7    1 2 3 4 3 2 1

%t 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[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[2500000,14] (* long evaluation time *)

%Y Cf. A174973, A237048, A237270, A237271, A237591, A237593, A238443, A249351 (widths), A250070, A262045, A341969, A341970, A341971, A347979.

%K nonn,more

%O 1,2

%A _Hartmut F. W. Hoft_, Sep 22 2021