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).

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).

Links

Table of n, a(n) for n=1..14.

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

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

Sequence in context: A105521 A154563 A325043 * A090073 A327089 A016728

Adjacent sequences: A338533 A338534 A338535 * A338537 A338538 A338539

Keyword

nonn,more

Author

Hartmut F. W. Hoft, Nov 01 2020

Status

approved