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

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(16,17,18,20,21,22,24,26,28) = (110880, 793800, 221760, 332640, 1587600, 554400, 831600, 720720, 1965600).

Examples

			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.
		

Crossrefs

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

Programs

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 *)