A133701 Triangle read by rows: T(n, k) = A001227(n) if k divides n, T(n, k) = 0 otherwise.

1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 2, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 0, 1, 3, 0, 3, 0, 0, 0, 0, 0, 3, 2, 2, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2

Offset

1,4

Links

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

Formula

Equals A133698 * A051731 as infinite lower triangular matrices.

Example

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

Prog

(PARI) T(n, k)=if(n%k, 0, numdiv(n>>valuation(n, 2))) \\ Andrew Howroyd, Sep 22 2025

Crossrefs

Column 1 and main diagonal are A001227.

Row sums are A335841.

Cf. A051731, A133698.

Sequence in context: A039976 A287267 A317540 * A230417 A287263 A102442

Adjacent sequences: A133698 A133699 A133700 * A133702 A133703 A133704

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 21 2007

Extensions

New name and a(56) onwards from Andrew Howroyd, Sep 22 2025

Status

approved