login
T(n, k) = sum_(1 <= j <= k) [j | k] j mu(k / j) gcd(n, k), triangle read by rows.
3

%I #12 Jul 13 2015 22:36:28

%S 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,

%T 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,

%U 110,1,2,6,8,4,12,6,16,18,8,10,48

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

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

%H Peter Luschny, Sequences related to <a href="http://www.oeis.org/wiki/User:Peter_Luschny/EulerTotient">Euler's totient</a> function.

%e 1

%e 1,2

%e 1,1,6

%e 1,2,2,8

%e 1,1,2,2,20

%e 1,2,6,4,4,12

%e 1,1,2,2,4,2,42

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

%t 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 *)

%Y Cf. Row sums of triangle A181540.

%K nonn,tabl

%O 1,3

%A _Peter Luschny_, Oct 29 2010