A181552 T(n,k) = gcd(n,k) A181549(k), triangle read by rows.

1, 1, 6, 1, 3, 12, 1, 6, 4, 20, 1, 3, 4, 5, 30, 1, 6, 12, 10, 6, 72, 1, 3, 4, 5, 6, 12, 56, 1, 6, 4, 20, 6, 24, 8, 80, 1, 3, 12, 5, 6, 36, 8, 10, 99, 1, 6, 4, 10, 30, 24, 8, 20, 11, 180, 1, 3, 4, 5, 6, 12, 8, 10, 11, 18, 132, 1, 6, 12, 20, 6, 72, 8, 40, 33, 36, 12, 240

Offset

1,3

Comments

A181549(n) = sum{k|n} k mu_2(n/k) is a variant of Euler's phi function relative to the Moebius function of order 2.

Links

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

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

Example

1,
1,6,
1,3,12,
1,6,.4,20,
1,3,.4,.5,30,
1,6,12,10,.6,72,
1,3,.4,.5,.6,12,56,
1,6,.4,20,.6,24,.8,80,

Maple

A181552 := (n, k) -> igcd(n, k)*A181549(k);

Mathematica

mu2[1] = 1; mu2[n_] := Sum[Boole[Divisible[n, d^2]]*MoebiusMu[n/d^2]*MoebiusMu[n/d], {d, Divisors[n]}]; A181549[n_] := Sum[k*mu2[n/k], {k, Divisors[n]}]; t[n_, k_] := GCD[n, k]*A181549[k]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 05 2014 *)

Crossrefs

Cf. A130212, A181538, row sums of triangle is A181553.

Sequence in context: A259731 A176399 A273081 * A294347 A229606 A101023

Adjacent sequences: A181549 A181550 A181551 * A181553 A181554 A181555

Keyword

nonn,tabl

Author

Peter Luschny, Oct 30 2010

Status

approved