OFFSET
1,2
COMMENTS
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
Multiplicative with a(p^e) = (p-1)*p if e=1, a(p^e)=0 if e>1.
Dirichlet g.f.: Sum_(n>=1) a(n)/n^s = Product_{primes p} (1-p^(1-s)+p^(2-s)).
From Vaclav Kotesovec, Jun 24 2020: (Start)
Dirichlet g.f.: zeta(s-2)*Product_{primes p} (1 + p^(3-2*s) - p^(4-2*s) - p^(1-s)).
Sum_{k=1..n} a(k) ~ c * n^3, where c = A065464/3 = 0.142749835... (End)
EXAMPLE
a(5) = 20 because 5 phi(5) |mu(5)| = 5 * 4 * |(-1)| = 20.
MATHEMATICA
Table[n EulerPhi[n] Abs[MoebiusMu[n]], {n, 60}] (* Alonso del Arte, Dec 20 2011 *)
f[p_, e_] := If[e == 1, (p-1)*p, 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 26 2020 *)
PROG
(PARI) a(n)=n*eulerphi(n)*abs(moebius(n)) \\ Charles R Greathouse IV, Dec 20 2011
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - p*X + p^2*X))[n], ", ")) \\ Vaclav Kotesovec, Jun 24 2020
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
R. J. Mathar, Dec 20 2011
STATUS
approved