A347979 a(n) is the smallest even number k whose symmetric representation of sigma(k) has maximum width n.

2, 6, 60, 120, 360, 840, 3360, 2520, 5040, 10080, 15120, 32760, 27720, 50400, 98280, 83160, 110880, 138600, 221760, 277200, 332640, 360360, 554400, 960960, 831600, 942480, 720720, 2217600, 1965600, 1441440

Offset: 1

Author

Hartmut F. W. Hoft, Sep 22 2021

Keywords

• nonn
• more

Comments

For the 30 known terms the symmetric representation of sigma consists of a single part, i.e., this is a subsequence of A174973 = A238443.

The sequence is not increasing with the maximum width of the symmetric representation of sigma.

Also a(33) = 2162160 is the only further number in the sequence less than 2500000.

Examples

			The pattern of maximum widths within the single part of the symmetric representation of sigma for the first four numbers in the sequence is:
  a(n) parts successive widths
    2:   1           1
    6:   1         1 2 1
   60:   1     1 2 3 2 3 2 1
  120:   1     1 2 3 4 3 2 1
		

Crossrefs

Cf. A174973, A237048, A237270, A237271, A237591, A237593, A238443, A249351 (widths), A250070, A262045, A341969, A341970, A341971, A347980.

Programs

Mathematica

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]]]
a347979[n_, mw_] := Module[{list=Table[0, mw], i, v}, For[i=2, i<=n, i+=2, v=Max[a262045[i]]; If [list[[v]]==0, list[[v]]=i]]; list]
a347979[2500000, 33] (* computes a(1..30), a(33); a(31..32) > 2500000 *)

Formula

It appears that a(n) = A250070(n) if n >= 2.