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

Author

Gary W. Adamson, Jan 17 2007

Keywords

• nonn
• tabl
• easy

Examples

			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;
...
		

Crossrefs

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

Programs

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

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).