A338535 -id:A338535 - cp's OEIS frontend

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

Hartmut F. W. Hoft, Nov 01 2020

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).

			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.

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

(* 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 *)

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.

Original entry on oeis.org

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

Offset: 1

Hartmut F. W. Hoft, Nov 01 2020

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).

			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.

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

(* 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 *)

cp's OEIS Frontend

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).

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