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

1,3

Links

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

Formula

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

Example

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.

Mathematica

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

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.

Sequence in context: A059016 A080418 A073892 * A332397 A004608 A366936

Adjacent sequences: A280345 A280346 A280347 * A280349 A280350 A280351

Keyword

nonn,tabf

Author

Omar E. Pol, Jan 09 2017

Status

approved