A144379 Triangle read by rows, first n terms of an array formed by A054521 * A054521(transform).

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

Offset

1,6

Comments

Right border = phi(n): (1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10,...).

Row sums = A125728: (1, 2, 4, 5, 10, 7, 18, 16, 23,...) = the number of positive integers less <=k coprime to both k and n.

Links

Table of n, a(n) for n=1..104.

Formula

Given A054521 as an infinite lower triangular matrix, perform A054521(transform). Multiply the result by A054521 getting an array, then extract the first n terms of each row to form a new triangle.

Example

A054521 * A054521(transform) =
1, 1, 1, 1, 1, 1, 1,...
1, 1, 1, 1, 1, 1, 1,...
1, 1, 2, 1, 2, 1, 2,...
1, 1, 1, 2, 2, 1, 2,...
1, 1, 2, 2, 4, 1, 4,...
...
Then extract the lower half of the array including the diagonal, A000010, phi(n); getting triangle A144379:
1;
1, 1;
1, 1, 2
1, 1, 1, 2;
1, 1, 2, 2, 4;
1, 1, 1, 1, 1, 2;
1, 1, 2, 2, 4, 2, 6;
1, 1, 1, 2, 2, 2, 3, 4;
1, 1, 2, 1, 3, 2, 4, 3, 6;
1, 1, 1, 2, 2, 1, 2, 3, 2, 4;
1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10;
...

Crossrefs

A054521, Cf. A000010, A125728

Sequence in context: A122191 A097847 A275120 * A337260 A296772 A228525

Adjacent sequences: A144376 A144377 A144378 * A144380 A144381 A144382

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 19 2008

Status

approved