A144379 - OEIS

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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

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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, 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, 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