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A163167 a(n) = sum_{d | phi(n)} mu( phi(d) ) * phi(n)/d, where phi = A000010. 2
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 (list; graph; refs; listen; history; text; internal format)
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): return sum([mobius(totient(d))*totient(n)/d for d in divisors(totient(n))])

print map(a, xrange(1, 101)) # Indranil Ghosh, Jul 17 2017

CROSSREFS

Cf. A000010, A008683, A074701, A289627.

Sequence in context: A046217 A057662 A015971 * A243729 A200810 A114003

Adjacent sequences:  A163164 A163165 A163166 * A163168 A163169 A163170

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Jul 22 2009

STATUS

approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)