A127527 Triangle T(n,k)= tau(k)*phi(n/k) if k|n, else T(n,k)=0.

1, 1, 2, 2, 0, 2, 2, 2, 0, 3, 4, 0, 0, 0, 2, 2, 4, 2, 0, 0, 4, 6, 0, 0, 0, 0, 0, 2, 4, 4, 0, 3, 0, 0, 0, 4, 6, 0, 4, 0, 0, 0, 0, 0, 3, 4, 8, 0, 0, 2, 0, 0, 0, 0, 4

Offset: 1

Author

Gary W. Adamson, Jan 17 2007

Keywords

• nonn
• tabl
• easy

Comments

Tau is the number of divisors A000005, and phi the Euler totient A000010.

Examples

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

Crossrefs

Cf. A054523, A000005, A000010, A000203.

Programs

Maple

A127527 := proc(n,k) if n mod k = 0 then numtheory[tau](k)*numtheory[phi](n/k) ; else 0; end if; end proc: # R. J. Mathar, Apr 11 2011

Formula

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

T(n,1) = A000010(n).

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

Sum_{k=1..n} T(n,k) = A000203(n).

Extensions

Definition clarified by R. J. Mathar, Apr 11 2011