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

1,1

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.

Links

Table of n, a(n) for n=1..30.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A316198 A074167 A083787 * A138286 A355286 A308532

Adjacent sequences: A347976 A347977 A347978 * A347980 A347981 A347982

Keyword

nonn,more

Author

Hartmut F. W. Hoft, Sep 22 2021

Status

approved