A319526 Square array read by antidiagonals upwards: T(n,k) = sigma(n*k), n >= 1, k >= 1.

1, 3, 3, 4, 7, 4, 7, 12, 12, 7, 6, 15, 13, 15, 6, 12, 18, 28, 28, 18, 12, 8, 28, 24, 31, 24, 28, 8, 15, 24, 39, 42, 42, 39, 24, 15, 13, 31, 32, 60, 31, 60, 32, 31, 13, 18, 39, 60, 56, 72, 72, 56, 60, 39, 18, 12, 42, 40, 63, 48, 91, 48, 63, 40, 42, 12, 28, 36, 72, 91, 90, 96, 96, 90, 91, 72, 36, 28

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Index entries for sequences related to sigma(n)

Formula

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

T(n,k) = A000203(A003991(n,k)).

Example

The corner of the square array begins:
A000203:    1,   3,   4,   7,   6,  12,   8,  15,  13,  18,  12,  28, ...
A062731:    3,   7,  12,  15,  18,  28,  24,  31,  39,  42,  36,  60, ...
A144613:    4,  12,  13,  28,  24,  39,  32,  60,  40,  72,  48,  91, ...
A193553:    7,  15,  28,  31,  42,  60,  56,  63,  91,  90,  84, 124, ...
A283118:    6,  18,  24,  42,  31,  72,  48,  90,  78,  93,  72, 168, ...
A224613:   12,  28,  39,  60,  72,  91,  96, 124, 120, 168, 144, 195, ...
A283078:    8,  24,  32,  56,  48,  96,  57, 120, 104, 144,  96, 224, ...
A283122:   15,  31,  60,  63,  90, 124, 120, 127, 195, 186, 180, 252, ...
A283123:   13,  39,  40,  91,  78, 120, 104, 195, 121, 234, 156, 280, ...
...

Mathematica

Table[DivisorSigma[1, # k] &[m - k + 1], {m, 12}, {k, m}] // Flatten (* Michael De Vlieger, Dec 31 2018 *)

Crossrefs

First 9 rows (also first 9 columns) are A000203, A062731, A144613, A193553, A283118, A224613, A283078, A283122, A283123.

Main diagonal gives A065764.

Cf. A000203, A003991, A216626, A319073.

Sequence in context: A318140 A266025 A216626 * A258835 A007448 A155689

Adjacent sequences: A319523 A319524 A319525 * A319527 A319528 A319529

Keyword

nonn,tabl

Author

Omar E. Pol, Sep 25 2018

Status

approved