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

1,2

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).

Links

Table of n, a(n) for n=1..18.

Example

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).

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 *)

Crossrefs

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

Sequence in context: A259139 A052615 A340506 * A250071 A192990 A276244

Adjacent sequences: A338532 A338533 A338534 * A338536 A338537 A338538

Keyword

nonn,more

Author

Hartmut F. W. Hoft, Nov 01 2020

Status

approved