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
Examples
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, ...
Links
- Seiichi Manyama, Antidiagonals n = 1..100, flattened
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.
Programs
-
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 *)