A379635 Triangle read by rows: T(n,k) = A000203(k)*A000203(n-k+1), n >= 1, k >= 1.

1, 3, 3, 4, 9, 4, 7, 12, 12, 7, 6, 21, 16, 21, 6, 12, 18, 28, 28, 18, 12, 8, 36, 24, 49, 24, 36, 8, 15, 24, 48, 42, 42, 48, 24, 15, 13, 45, 32, 84, 36, 84, 32, 45, 13, 18, 39, 60, 56, 72, 72, 56, 60, 39, 18, 12, 54, 52, 105, 48, 144, 48, 105, 52, 54, 12, 28, 36, 72, 91, 90, 96, 96, 90, 91, 72, 36, 28

Offset: 1

Author

Omar E. Pol, Jan 14 2025

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1;
   3,   3;
   4,   9,   4;
   7,  12,  12,   7;
   6,  21,  16,  21,   6;
  12,  18,  28,  28,  18,  12;
   8,  36,  24,  49,  24,  36,   8;
  15,  24,  48,  42,  42,  48,  24,  15;
  13,  45,  32,  84,  36,  84,  32,  45,  13;
  18,  39,  60,  56,  72,  72,  56,  60,  39,  18;
  12,  54,  52, 105,  48, 144,  48, 105,  52,  54,  12;
  28,  36,  72,  91,  90,  96,  96,  90,  91,  72,  36,  28;
  14,  84,  48, 126,  78, 180,  64, 180,  78, 126,  48,  84,  14;
  ...
For n = 10 the calculation of the row 10 is as follows:
    k    A000203         T(10,k)
    1       1   *  18   =   18
    2       3   *  13   =   39
    3       4   *  15   =   60
    4       7   *   8   =   56
    5       6   *  12   =   72
    6      12   *   6   =   72
    7       8   *   7   =   56
    8      15   *   4   =   60
    9      13   *   3   =   39
   10      18   *   1   =   18
                 A000203
.
		

Links

• Index entries for sequences related to sigma(n).

Crossrefs

Column 1 and leading diagonal give A000203.

Middle diagonal gives A072861.

Row sums give A000385.

Cf. A221529.

Programs

Mathematica

T[n_,k_]:=DivisorSigma[1,k]*DivisorSigma[1,n-k+1];Table[T[n,k],{n,12},{k,n }]//Flatten (* James C. McMahon, Jan 15 2025 *)

PARI

T(n, k)=sigma(k)*sigma(n-k+1)