

A202535


n*phi(n)*abs( mobius(n) ).


2



1, 2, 6, 0, 20, 12, 42, 0, 0, 40, 110, 0, 156, 84, 120, 0, 272, 0, 342, 0, 252, 220, 506, 0, 0, 312, 0, 0, 812, 240, 930, 0, 660, 544, 840, 0, 1332, 684, 936, 0, 1640, 504, 1806, 0, 0, 1012, 2162, 0, 0, 0, 1632, 0, 2756, 0, 2200, 0, 2052, 1624, 3422
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The inverse Mobius transform is b(n>=1) = 1, 3, 7, 3, 21, 21, 43, 3,7, 63, 11, 21,...., multiplicative with b(p^e) = A002061(p), e>=1 (see A119959).  Mathar
a(n) > 0 only when n is squarefree.  Alonso del Arte, Dec 20 2011


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = A002618(n) *A008966(n).
Multiplicative with a(p^e) = (p1)*p if e=1, a(p^e)=0 if e>1.
Dirichlet g.f. sum_(n>=1) a(n)/n^s = product_{primes p} (1p^(1s)+p^(2s)).


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 *)


PROG

(PARI) a(n)=n*eulerphi(n)*abs(moebius(n)) \\ Charles R Greathouse IV, Dec 20 2011


CROSSREFS

Cf. A079579.
Sequence in context: A243015 A139717 A285119 * A138703 A106458 A213323
Adjacent sequences: A202532 A202533 A202534 * A202536 A202537 A202538


KEYWORD

nonn,mult,easy


AUTHOR

R. J. Mathar, Dec 20 2011


STATUS

approved



