A163167 a(n) = sum_{d | phi(n)} mu( phi(d) ) * phi(n)/d, where phi = A000010.

1, 1, 3, 3, 5, 3, 6, 5, 6, 5, 15, 5, 9, 6, 10, 10, 20, 6, 21, 10, 9, 15, 36, 10, 25, 9, 21, 9, 41, 10, 30, 20, 25, 20, 18, 9, 33, 21, 18, 20, 50, 9, 51, 25, 18, 36, 72, 20, 51, 25, 40, 18, 65, 21, 50, 18, 33, 41, 87, 20, 45, 30, 33, 40, 36, 25, 75, 40, 61, 18, 120, 18, 66, 33, 50, 33

Offset

1,3

Comments

Fixed points are in A074701.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Formula

a(n) = A289627(A000010(n)). - Antti Karttunen, Jul 17 2017

Maple

with(numtheory):
A163167:=proc(n)
    local div:
    div:=convert(divisors(phi(n)), list):
    add( mobius(phi(d))*phi(n)/d, d=div) ;
end proc:
seq(A163167(n), n=1..120) ;

Mathematica

Table[Sum[MoebiusMu[EulerPhi[d]] EulerPhi[n]/d, {d, Divisors[EulerPhi[n]]}], {n, 100}] (* Indranil Ghosh, Jul 17 2017 *)

Prog

(PARI) A163167(n) = sumdiv(eulerphi(n), d, moebius(eulerphi(d))*eulerphi(n)/d); \\ Antti Karttunen, Jul 17 2017
(PARI)
A289627(n) = sumdiv(n, d, moebius(eulerphi(d))*n/d);
A163167(n) = A289627(eulerphi(n)); \\ Antti Karttunen, Jul 17 2017
(Python)
from sympy import mobius, totient, divisors
def a(n):
    tn = totient(n)
    return sum(mobius(totient(d))*tn//d for d in divisors(tn))
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Jul 17 2017

Crossrefs

Cf. A000010, A008683, A074701, A289627.

Sequence in context: A046217 A057662 A015971 * A243729 A200810 A365710

Adjacent sequences: A163164 A163165 A163166 * A163168 A163169 A163170

Keyword

easy,nonn

Author

R. J. Mathar, Jul 22 2009

Status

approved