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A347979
a(n) is the smallest even number k whose symmetric representation of sigma(k) has maximum width n.
5
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.
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 *)
KEYWORD
nonn,more
AUTHOR
Hartmut F. W. Hoft, Sep 22 2021
STATUS
approved