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A181549 Sum{k|n} k mu_2(n/k) 3
0, 1, 3, 4, 5, 6, 12, 8, 10, 11, 18, 12, 20, 14, 24, 24, 20, 18, 33, 20, 30, 32, 36, 24, 40, 29, 42, 33, 40, 30, 72, 32, 40, 48, 54, 48, 55, 38, 60, 56, 60, 42, 96, 44, 60, 66, 72, 48, 80, 55, 87, 72, 70, 54, 99, 72, 80, 80, 90, 60 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sum{k|n} k mu(n/k) is Euler's phi function. In A181549 mu(n) is replaced by the Moebius function of order 2, mu_2(n), A189021(n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

MAPLE

A181549 := proc(n) local k; add(k*A189021(n/k), k=divisors(n)) end;

MATHEMATICA

mu2[1] = 1; mu2[n_] := Sum[Boole[Divisible[n, d^2]]*MoebiusMu[n/d^2]*MoebiusMu[n/d], {d, Divisors[n]}]; a[n_] := Sum[k*mu2[n/k], {k, Divisors[n]}]; Table[a[n], {n, 0, 59}] (* Jean-François Alcover, Feb 05 2014 *)

CROSSREFS

Cf. A008683, A181550, A181552, A181553.

Sequence in context: A191750 A034448 A069184 * A241405 A049417 A188999

Adjacent sequences:  A181546 A181547 A181548 * A181550 A181551 A181552

KEYWORD

nonn,mult

AUTHOR

Peter Luschny, Oct 30 2010

STATUS

approved

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Last modified December 12 23:59 EST 2018. Contains 318081 sequences. (Running on oeis4.)