A127465 Triangle read by rows: T(n,k) = k*phi(n/k) if k|n, T(n,k)=0 otherwise.

1, 1, 2, 2, 0, 3, 2, 2, 0, 4, 4, 0, 0, 0, 5, 2, 4, 3, 0, 0, 6, 6, 0, 0, 0, 0, 0, 7, 4, 4, 0, 4, 0, 0, 0, 8, 6, 0, 6, 0, 0, 0, 0, 0, 9, 4, 8, 0, 0, 5, 0, 0, 0, 0, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 4, 4, 6, 8, 0, 6, 0, 0, 0, 0, 0, 12

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)

Formula

T(n,k) = k*A054523(n,k).

Example

First few rows of the triangle are:
1;
1, 2;
2, 0, 3;
2, 2, 0, 4;
4, 0, 0, 0, 5;
2, 4, 3, 0, 0, 6;
6, 0, 0, 0, 0, 0, 7;
4, 4, 0, 4, 0, 0, 0, 8;
...

Maple

A127465 := proc(n, k)
        if n mod k = 0 then
                k*numtheory[phi](n/k) ;
        else
                0;
        end if;
end proc:
seq(seq(A127465(n, m), m=1..n), n=1..12) ; # R. J. Mathar, Nov 08 2011

Crossrefs

Cf. A054523, A000010 (column k=1), A018804 (row sums).

Sequence in context: A324518 A108807 A129236 * A339033 A327028 A271707

Adjacent sequences: A127462 A127463 A127464 * A127466 A127467 A127468

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jan 15 2007

Status

approved