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.

882, 990, 7938, 2100, 22050, 13200, 63504, 12600, 304200, 32760, 88200, 102960

Offset: 1

Author

Hartmut F. W. Hoft, Nov 01 2020

Keywords

• nonn
• more

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).

Examples

			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.
		

Crossrefs

Cf. A235791, A237048, A237270, A237591, A237593, A249223, A338535, A338536.

Programs

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 *)