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A338536
a(n) is the smallest number k for which the width n at the diagonal is one smaller than the maximum width of the symmetric representation of sigma(k).
2
18, 60, 900, 360, 1800, 3360, 14400, 5040, 44100, 15120, 508032, 27720, 396900, 98280
OFFSET
1,1
COMMENTS
All numbers computed so far for this sequence have a symmetric representation of sigma that consists of a single region.
Additional values computed through 2000000 are a(16,17,18,20,21,22,24,26,28) = (110880, 793800, 221760, 332640, 1587600, 554400, 831600, 720720, 1965600).
EXAMPLE
a(2) = 60 = 2*2*3*5 is in the sequence since it is the smallest with width 2 at the diagonal and maximum width 3 in its symmetric representation of sigma. The widths of its 10 legs to the diagonal are: 1, 1, 2, 2, 3, 3, 3, 2, 2, 2.
MATHEMATICA
(* Functions row[] and a237048[] are defined in A237048 *)
widthQ1[n_] := Module[{r=row[n], cW=0, mW=0, k}, For[k=1, k<=r, k++, cW+=(-1)^(k+1) a237048[n, k]; If[cW>mW, mW=cW]]; If[mW==cW+1 && cW>0, cW, 0]]
a338536[n_, b_] := Module[{list=Table[0, {b}], k, wQ}, For[k=1, k<=n, k++, wQ=widthQ1[k]; If[wQ!=0&&list[[wQ]]==0, list[[wQ]]=k]]; list]
Take[a338536[1000000, 20], 14] (* sequence data *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Hartmut F. W. Hoft, Nov 01 2020
STATUS
approved