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A338538
a(n) is the smallest number k for which the width n at the diagonal is two smaller than the maximum width of the symmetric representation of sigma(k), the sum of divisors of k.
1
882, 990, 7938, 2100, 22050, 13200, 63504, 12600, 304200, 32760, 88200, 102960
OFFSET
1,1
COMMENTS
All numbers computed so far for this sequence have a symmetric representation of sigma that consists of a single region; see A237270 and A237593.
Additional values computed through 2000000 are a(14,15,16,17,18,20,22,24,28) = (171360, 1960200, 240240, 705600, 327600, 957600, 1375920, 1108800, 1663200).
EXAMPLE
a(1) = 882 = 2*3^2*7^2 is in the sequence since it is the smallest with maximum width 3 and width 1 at the diagonal. The widths of its 41 legs to the diagonal are: 1..2..1..2..3..2..3..2..1.
MATHEMATICA
(* Functions row[] and a237048[] are defined in A237048 *)
widthQ2[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+2 && cW>0, cW, 0]]
a338538[n_, b_] := Module[{list=Table[0, {b}], k, wQ}, For[k=1, k<=n, k++, wQ=widthQ2[k]; If[wQ!=0&&list[[wQ]]==0, list[[wQ]]=k]]; list]
Take[a338538[1000000, 20], 12] (* sequence data *)
KEYWORD
nonn,more
AUTHOR
Hartmut F. W. Hoft, Nov 01 2020
STATUS
approved