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A074722 a(n) = Sum_{d divides n} phi(n/d)*(-1)^bigomega(d). 2
1, 0, 1, 2, 3, 0, 5, 2, 5, 0, 9, 2, 11, 0, 3, 6, 15, 0, 17, 6, 5, 0, 21, 2, 17, 0, 13, 10, 27, 0, 29, 10, 9, 0, 15, 10, 35, 0, 11, 6, 39, 0, 41, 18, 15, 0, 45, 6, 37, 0, 15, 22, 51, 0, 27, 10, 17, 0, 57, 6, 59, 0, 25, 22, 33, 0, 65, 30, 21, 0, 69, 10, 71, 0, 17, 34, 45, 0, 77, 18, 41, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

a(n) = 0 if and only if n == 2 (mod 4). - Robert Israel, Jan 04 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Multiplicative with a(p^e) = 2*(-1)^(e+1)*((-p)^(e+1)-1)/(p+1)-p^e.

Dirichlet g.f.: zeta(2s)*zeta(s-1)/(zeta(s)^2). - Benedict W. J. Irwin, Jul 11 2018

Sum_{k=1..n} a(k) ~ n^2 / 5. - Vaclav Kotesovec, Feb 01 2019

MAPLE

f:= proc(n) uses numtheory; local d;

   add(phi(n/d)*(-1)^bigomega(d), d=divisors(n))

end proc:

map(f, [$1..100]); # Robert Israel, Jan 04 2017

MATHEMATICA

f[d_] := EulerPhi[n/d] LiouvilleLambda[d]

Table[DivisorSum[n, f], {n, 1, 50}] (* Benedict W. J. Irwin, Jul 11 2018 *)

PROG

(PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*(-1)^bigomega(d)); \\ Michel Marcus, Jul 11 2018

CROSSREFS

Cf. A000010, A001222, A058026.

Sequence in context: A071322 A072594 A272591 * A080368 A057174 A197658

Adjacent sequences:  A074719 A074720 A074721 * A074723 A074724 A074725

KEYWORD

mult,nonn

AUTHOR

Vladeta Jovovic, Sep 27 2002

STATUS

approved

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Last modified October 16 05:38 EDT 2019. Contains 328044 sequences. (Running on oeis4.)