A143614 Triangle read by rows: A054521 * A051731 as infinite lower triangular matrices.

1, 1, 0, 2, 1, 0, 2, 0, 1, 0, 4, 2, 1, 1, 0, 2, 0, 0, 0, 1, 0, 6, 3, 2, 1, 1, 1, 0, 4, 0, 1, 0, 1, 0, 1, 0, 6, 3, 0, 2, 1, 0, 1, 1, 0, 4, 0, 2, 0, 0, 0, 1, 0, 1, 0, 10, 5, 3, 2, 2, 1, 1, 1, 1, 1, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 6, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0

Offset

1,4

Comments

Left border = phi(n), A000010: (1, 1, 2, 2, 4, 2, 6,...).

Row sums = A143615: (1, 1, 3, 3, 8, 3, 14, 7,...).

Links

Table of n, a(n) for n=1..105.

Formula

A054521 records the relative primes of n, indicated by a 1's in row n, 0 otherwise. A051731 = the inverse Moebius transform, in which 1's by rows indicate the divisors of n, 0 otherwise.

Example

First few rows of the triangle =
1;
1, 0;
2, 1, 0;
2, 0, 1, 0;
4, 2, 1, 1, 0;
2, 0, 0, 0, 1, 0;
6, 3, 2, 1, 1, 1, 0;
4, 0, 1, 0, 1, 0, 1, 0;
6, 3, 0, 2, 1, 0, 1, 1, 0;
...

Crossrefs

Cf. A000010, A051731, A054521, A143615.

Sequence in context: A366768 A137696 A275731 * A071412 A080884 A354452

Adjacent sequences: A143611 A143612 A143613 * A143615 A143616 A143617

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 27 2008

Extensions

a(96) and a(101) split by Georg Fischer, May 29 2023

Status

approved