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

1,3

Comments

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

Links

Table of n, a(n) for n=1..78.

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

Example

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

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 *)

Crossrefs

Cf. Row sums of triangle A181540.

Sequence in context: A333144 A306297 A053383 * A322128 A125731 A123361

Adjacent sequences: A181535 A181536 A181537 * A181539 A181540 A181541

Keyword

nonn,tabl

Author

Peter Luschny, Oct 29 2010

Status

approved