A181538 T(n, k) = sum_(1 <= j <= k) [j | k] j mu(k / j) gcd(n, k), triangle read by rows.

1, 1, 2, 1, 1, 6, 1, 2, 2, 8, 1, 1, 2, 2, 20, 1, 2, 6, 4, 4, 12, 1, 1, 2, 2, 4, 2, 42, 1, 2, 2, 8, 4, 4, 6, 32, 1, 1, 6, 2, 4, 6, 6, 4, 54, 1, 2, 2, 4, 20, 4, 6, 8, 6, 40, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 110, 1, 2, 6, 8, 4, 12, 6, 16, 18, 8, 10, 48

Offset: 1

Author

Peter Luschny, Oct 29 2010

Keywords

• nonn
• tabl

Comments

T(n,k) = gcd(n,k) phi(k). Can be seen as a generalization of n -> phi(n^2) [A002618].

Examples

			1
1,2
1,1,6
1,2,2,8
1,1,2,2,20
1,2,6,4,4,12
1,1,2,2,4,2,42
		

Links

• Peter Luschny, Sequences related to Euler's totient function.

Crossrefs

Cf. Row sums of triangle A181540.

Programs

Maple

A181538 := (n,k) -> igcd(n,k)*phi(k);

Mathematica

t[n_, k_] := Block[{j = Divisors@ k}, Plus @@ (#*MoebiusMu[k/#] & /@ j)] GCD[n, k]; Table[ t[n, k], {n, 12}, {k, n}] // Flatten (* Robert G. Wilson v, Jan 19 2011 *)