

A319998


a(n) = Sum_{dn, d is even} mu(n/d)*d, where mu(n) is Moebius function A008683.


4



0, 2, 0, 2, 0, 4, 0, 4, 0, 8, 0, 4, 0, 12, 0, 8, 0, 12, 0, 8, 0, 20, 0, 8, 0, 24, 0, 12, 0, 16, 0, 16, 0, 32, 0, 12, 0, 36, 0, 16, 0, 24, 0, 20, 0, 44, 0, 16, 0, 40, 0, 24, 0, 36, 0, 24, 0, 56, 0, 16, 0, 60, 0, 32, 0, 40, 0, 32, 0, 48, 0, 24, 0, 72, 0, 36, 0, 48, 0, 32, 0, 80, 0, 24, 0, 84, 0, 40, 0, 48, 0, 44, 0, 92, 0, 32, 0, 84, 0, 40, 0, 64, 0, 48, 0
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OFFSET

1,2


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..20000


FORMULA

a(n) = Sum_{dn} A059841(d)*A008683(n/d)*d.
a(n) = A000010(n)  A319997(n).
a(2n) = 2*A000010(n), a(2n+1) = 0.
G.f.: Sum_{k>=1} 2*mu(k)*x^(2*k)/(1  x^(2*k))^2.  Ilya Gutkovskiy, Nov 02 2018


MATHEMATICA

Rest[CoefficientList[Series[Sum[2*MoebiusMu[k]*x^(2*k)/(1  x^(2*k))^2, {k, 1, 100}], {x, 0, 100}], x]] (* Vaclav Kotesovec, Nov 03 2018 *)


PROG

(PARI) A319998(n) = sumdiv(n, d, (!(d%2))*moebius(n/d)*d);
(PARI) A319998(n) = if(n%2, 0, 2*eulerphi(n/2));


CROSSREFS

Cf. A000010, A140434, A146076, A319997.
Sequence in context: A111813 A167156 A132952 * A029187 A201863 A035385
Adjacent sequences: A319995 A319996 A319997 * A319999 A320000 A320001


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 31 2018


STATUS

approved



