A280348 Irregular triangle read by rows in which row n lists the divisors of the sum of the divisors of n.

1, 1, 3, 1, 2, 4, 1, 7, 1, 2, 3, 6, 1, 2, 3, 4, 6, 12, 1, 2, 4, 8, 1, 3, 5, 15, 1, 13, 1, 2, 3, 6, 9, 18, 1, 2, 3, 4, 6, 12, 1, 2, 4, 7, 14, 28, 1, 2, 7, 14, 1, 2, 3, 4, 6, 8, 12, 24, 1, 2, 3, 4, 6, 8, 12, 24, 1, 31, 1, 2, 3, 6, 9, 18, 1, 3, 13, 39, 1, 2, 4, 5, 10, 20, 1, 2, 3, 6, 7, 14, 21, 42, 1, 2, 4, 8, 16, 32, 1, 2, 3, 4, 6, 9, 12, 18, 36

Offset: 1

Author

Omar E. Pol, Jan 09 2017

Keywords

• nonn
• tabf

Examples

			Triangle begins:
1;
1, 3;
1, 2, 4;
1, 7;
1, 2, 3, 6;
1, 2, 3, 4, 6, 12;
1, 2, 4, 8;
1, 3, 5, 15;
1, 13;
1, 2, 3, 6, 9, 18;
1, 2, 3, 4, 6, 12;
1, 2, 4, 7, 14, 28;
1, 2, 7, 14;
1, 2, 3, 4, 6, 8, 12, 24;
1, 2, 3, 4, 6, 8, 12, 24;
1, 31;
1, 2, 3, 6, 9, 18;
1, 3, 13, 39;
1, 2, 4, 5, 10, 20;
1, 2, 3, 6, 7, 14, 21, 42;
1, 2, 4, 8, 16, 32;
1, 2, 3, 4, 6, 9, 12, 18, 36;
1, 2, 3, 4, 6, 8, 12, 24;
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60;
...
For n = 10 the sum of the divisors of 10 is 1 + 2 + 5 + 10 = 18, so row 10 of the triangle lists the divisors of 18: 1, 2, 3, 6, 9, 18.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..11428 (rows 1..700 of triangle, flattened).

Crossrefs

Right border gives A000203.

Row sums give A051027.

Row lengths give A062068.

Row products give A280581.

Column 1 is A000012.

Column 2 gives A071189, n >= 2.

Cf. A000005, A027750.

Programs

Mathematica

Divisors[DivisorSigma[1, Range[25]]] (* Paolo Xausa, Dec 11 2024 *)

Formula

T(n,k) = A027750(A000203(n),k).