A133699 Triangle read by rows: T(n, k) = A001227(k) if k divides n, T(n, k) = 0 otherwise.

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

Offset

1,6

Links

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

Formula

Equals A051731 * A133698, as infinite lower triangular matrices.

T(n,k) = A051731(n,k) * A001227(k). - Andrew Howroyd, Sep 25 2025

Example

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

Prog

(PARI) T(n, k)=if(n%k, 0, numdiv(k>>valuation(k, 2))) \\ Andrew Howroyd, Sep 25 2025

Crossrefs

Main diagonal is A001227.

Row sums are A133700.

Cf. A051731, A133698, A133701.

Sequence in context: A271592 A357187 A128409 * A157361 A369454 A224444

Adjacent sequences: A133696 A133697 A133698 * A133700 A133701 A133702

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 21 2007

Extensions

New name and a(56) onwards from Andrew Howroyd, Sep 25 2025

Status

approved