A129559 Triangle read by rows: A054523 * A115361 as infinite lower triangular matrices.

1, 2, 1, 2, 0, 1, 4, 2, 0, 1, 4, 0, 0, 0, 1, 4, 2, 2, 0, 0, 1, 6, 0, 0, 0, 0, 0, 1, 8, 4, 0, 2, 0, 0, 0, 1, 6, 0, 2, 0, 0, 0, 0, 0, 1, 8, 4, 0, 0, 2, 0, 0, 0, 0, 1, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 4, 4, 2, 0, 2, 0, 0, 0, 0, 0, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1,2

Links

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

Formula

Equals A054523 * A115361 as infinite lower triangular matrices.

T(n,k) = phi(2*n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 07 2018

Example

First few rows of the triangle:
  1;
  2, 1;
  2, 0, 1;
  4, 2, 0, 1;
  4, 0, 0, 0, 1;
  4, 2, 2, 0, 0, 1;
  6, 0, 0, 0, 0, 0, 1;
  8, 4, 0, 2, 0, 0, 0, 1;
  ...

Prog

(PARI) T(n, k)=if(n%k, 0, eulerphi(2*n/k)) \\ Andrew Howroyd, Aug 07 2018

Crossrefs

Column 1 is A062570.

Row sums are A129527 (inverse Moebius transform of A062570).

Cf. A054523, A115361.

Sequence in context: A156837 A255935 A374394 * A129680 A391261 A118231

Adjacent sequences: A129556 A129557 A129558 * A129560 A129561 A129562

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 20 2007

Extensions

Terms a(56) and beyond from Andrew Howroyd, Aug 07 2018

Status

approved