A127528 Triangle T(n,k) read by rows: tau(n)*phi(n/k) if k|n, else 0.

1, 2, 2, 4, 0, 2, 6, 3, 0, 3, 8, 0, 0, 0, 2, 8, 8, 4, 0, 0, 4, 12, 0, 0, 0, 0, 0, 2, 16, 8, 0, 4, 0, 0, 0, 4, 18, 0, 6, 0, 0, 0, 0, 0, 3, 16, 16, 0, 0, 4, 0, 0, 0, 0, 4, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 24, 12, 12, 12, 0, 6, 0, 0, 0, 0, 0, 6, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 24, 24

Offset

1,2

Links

Table of n, a(n) for n=1..93.

Formula

T(n,k) = A000005(n) * A054523(n,k).

T(n,1) = A062355(n).

T(n,n) = A000005(n).

sum_{k=1..n} T(n,k) = A038040(n).

Example

First few rows of the triangle are:
1;
2, 2;
4, 0, 2;
6, 3, 0, 3;
8, 0, 0, 0, 2;
8, 8, 4, 0, 0, 4;
12, 0, 0, 0, 0, 0, 2;
...

Maple

A127528 := proc(n, k) if n mod k = 0 then numtheory[tau](n)*numtheory[phi](n/k) ; else  0; end if; end proc:
seq(seq(A127528(n, k), k=1..n), n=1..15) ; # R. J. Mathar, Feb 05 2011

Crossrefs

Cf. A054523, A127527, A062355, A038040, A000005.

Sequence in context: A279906 A246846 A292474 * A063070 A049802 A129240

Adjacent sequences: A127525 A127526 A127527 * A127529 A127530 A127531

Keyword

nonn,tabl,easy

Author

Gary W. Adamson, Jan 17 2007

Status

approved