A181550 T(n,k) = floor(n/k)*A181549(k), triangle read by rows.

1, 2, 3, 3, 3, 4, 4, 6, 4, 5, 5, 6, 4, 5, 6, 6, 9, 8, 5, 6, 12, 7, 9, 8, 5, 6, 12, 8, 8, 12, 8, 10, 6, 12, 8, 10, 9, 12, 12, 10, 6, 12, 8, 10, 11, 10, 15, 12, 10, 12, 12, 8, 10, 11, 18, 11, 15, 12, 10, 12, 12, 8, 10, 11, 18, 12, 12, 18, 16, 15, 12, 24, 8, 10, 11, 18, 12, 20

Offset

1,2

Comments

A181549(n) = sum{k|n} k mu_2(n/k), 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
2, 3
3, 3, 4
4, 6, 4, 5
5, 6, 4, 5, 6
6, 9, 8, 5, 6, 12
7, 9, 8, 5, 6, 12, 8
8, 12, 8, 10, 6, 12, 8, 10

Maple

A181550 := (n, k) -> iquo(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_] := Floor[n/k]*A181549[k]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 05 2014 *)

Crossrefs

Cf. A130212, A181549.

Sequence in context: A156250 A029108 A350812 * A134841 A071112 A097087

Adjacent sequences: A181547 A181548 A181549 * A181551 A181552 A181553

Keyword

nonn,tabl

Author

Peter Luschny, Oct 30 2010

Status

approved