A327785 Square array read by antidiagonals: A(n,k) = Sum_{d|n} (k/d), (n>=1, k>=0), where (m/n) is the Kronecker symbol.

1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 0, 0, 3, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 0, 4, 1, 1, 1, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 0, 2, 4, 1, 1, 1, 2, 1, 1, 2, 0, 1, 3, 1, 1, 2, 0, 3, 2, 0, 2, 0, 1, 4, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 2, 3, 0, 4, 0, 0, 3, 0, 0, 6, 1

Offset

1,5

Links

Seiichi Manyama, Antidiagonals n = 1..100, flattened

Example

Square array begins:
   1, 1, 1, 1, 1, 1, 1, 1, ...
   1, 2, 1, 0, 1, 0, 1, 2, ...
   1, 2, 0, 1, 2, 0, 1, 2, ...
   1, 3, 1, 1, 1, 1, 1, 3, ...
   1, 2, 0, 0, 2, 1, 2, 0, ...
   1, 4, 0, 0, 2, 0, 1, 4, ...
   1, 2, 2, 0, 2, 0, 0, 1, ...
   1, 4, 1, 0, 1, 0, 1, 4, ...

Mathematica

A[n_, k_] := Sum[KroneckerSymbol[k, d], {d, Divisors[n]}];
Table[A[n - k, k], {n, 1, 13}, {k, n - 1, 0, -1}] // Flatten (* Jean-François Alcover, Sep 25 2019 *)

Crossrefs

Columns k=0..31 give A000012, A000005, A035185, A035186, A001227, A035187, A035188, A035189, A035185, A035191, A035192, A035193, A035194, A035195, A035196, A035197, A001227, A035199, A035200, A035201, A035202, A035203, A035204, A035205, A035188, A035207, A035208, A035186, A035210, A035211, A035212, A035213.

Cf. A215200.

Sequence in context: A365658 A116861 A340032 * A105242 A336709 A221362

Adjacent sequences: A327782 A327783 A327784 * A327786 A327787 A327788

Keyword

nonn,tabl

Author

Seiichi Manyama, Sep 25 2019

Status

approved