A338535 a(n) is the smallest number k for which the width n at the diagonal equals the maximum width of the symmetric representation of sigma(k).

1, 6, 72, 120, 3528, 840, 3600, 2520, 28800, 10080, 129600, 36960, 259200, 50400, 176400, 83160, 352800, 138600

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.

Additional values computed through 2000000 are a(20,21,22,24,26,30) = (277200, 1411200, 360360, 960960, 942480, 1884960).

Examples

			a(3) = 72 = 2^3*3^2 is in the sequence since it is the smallest with maximum width 3 and width 3 at the diagonal for its symmetric representation of sigma. Number 60 is the smallest number with maximum width 3, but it has width 2 at the diagonal (see also Ax22222). a(3) has the following pattern for the widths of the legs up to the diagonal (see A249223): 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3 for its single region.
a(5) = 3528 = 2^3*3^2*7^2 is in the sequence, but does not have a monotone increase of widths up to the diagonal in its single region: 1...2...3...4...3...4...3...4...5 (there are 83 legs to the diagonal).
		

Crossrefs

Cf. A128605, A235791, A237048, A237591, A237593, A249223, A250071.

Programs

Mathematica

(* Functions row[] and a237048[] are defined in A237048 *)
widthQ0[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, cW, 0]]
a338535[n_, b_] := Module[{list=Table[0, {b}], k, wQ}, For[k=1, k<=n, k++, wQ=widthQ0[k]; If[wQ!=0&&list[[wQ]]==0, list[[wQ]]=k]]; list]
Take[a338535[500000,25],18] (* sequence data *)