A129559 A054523 * A115361.

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

Author

Gary W. Adamson, Apr 20 2007

Keywords

• nonn
• tabl

Comments

row sums = A129527: (1, 3, 3, 7, 5, 9, 7, 15, ...). Left column = phi(2*n), A062570: (1, 2, 2, 4, 4, 4, 6, 8, ...).

Examples

			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;
  ...
		

Links

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

Crossrefs

Column 1 is A062570.

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

Cf. A054523, A115361.

Programs

PARI

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

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

Extensions

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