A130210 Triangle read by rows: T(n, k) = A000005(k) if k divides n, T(n, k) = 0 otherwise.

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

Offset

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

Formula

Equals A051731 * A130209 as infinite lower triangular matrices.

T(n,n) = A000005(n).

T(n,k) = A051731(n,k) * A000005(k). - Andrew Howroyd, Sep 25 2025

Example

First few rows of the triangle are:
  1;
  1, 2;
  1, 0, 2;
  1, 2, 0, 3;
  1, 0, 0, 0, 2;
  1, 2, 2, 0, 0, 4;
  1, 0, 0, 0, 0, 0, 2;
  ...

Maple

A130210 := proc(n, k)
    add( A051731(n, j)*A130209(j, k), j=k..n) ;
end proc:
seq(seq(A130210(n, k), k=1..n), n=1..15) ;  # R. J. Mathar, Aug 06 2016

Prog

(PARI) T(n, k)=if(n%k, 0, numdiv(k)) \\ Andrew Howroyd, Sep 25 2025

Crossrefs

Main diagonal is A000005.

Row sums are A007425.

Cf. A051731, A130209, A130277.

Sequence in context: A230025 A330374 A207869 * A236459 A190427 A287108

Adjacent sequences: A130207 A130208 A130209 * A130211 A130212 A130213

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, May 17 2007

Extensions

New name from Andrew Howroyd, Sep 25 2025

Status

approved