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A007431
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Sum_{d|n} phi(d)*mu(n/d).
(Formerly M2197)
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6
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0, 1, 0, 1, 1, 3, 0, 5, 2, 4, 0, 9, 1, 11, 0, 3, 4, 15, 0, 17, 3, 5, 0, 21, 2, 16, 0, 12, 5, 27, 0, 29, 8, 9, 0, 15, 4, 35, 0, 11, 6, 39, 0, 41, 9, 12, 0, 45, 4, 36, 0, 15, 11, 51, 0, 27, 10, 17, 0, 57, 3, 59, 0, 20, 16, 33, 0, 65, 15, 21, 0, 69, 8, 71, 0, 16, 17, 45, 0, 77, 12, 36, 0, 81, 5, 45, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Also Moebius transform applied twice to natural numbers.
Also number of complex primitive Dirichlet characters modulo n and sum(k=1,n,a(k)) is asymptotic to (18/pi^4)*n^2. - S. R. Finch (Steven.Finch(AT)inria.fr), Feb 16 2006
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REFERENCES
| H. Jager, On the number of Dirichlet characters with modulus not exceeding x, Nederl. Akad. Wetensch. Proc. Ser. A 76=Indag. Math. 35 (1973) 452-455.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
N. J. A. Sloane, Transforms
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FORMULA
| Multiplicative with a(p)=p-2 and a(p^e)=p^e-2*p^(e-1)+p^(e-2) for e>1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 25 2002
Dirichlet g.f.: zeta(x-1)/zeta^2(x)
n>0, a(n)=sum(k=1,n,mu(gcd(n,k))) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 14 2007
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MAPLE
| with(numtheory); f:=n->add( phi(d)*mobius(n/d), d in divisors(n)); [seq(f(n), n=0..120)];
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MATHEMATICA
| Table[Sum[EulerPhi[d] MoebiusMu[n/d], {d, Divisors[n]}], {n, 0, 86}] (* Jean-François Alcover, Apr 04 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 0, direuler(p=2, n, (1-X)^2/(1-p*X))[n]) (from R. Stephan)
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CROSSREFS
| Sequence in context: A130054 A187886 A196111 * A159980 A098496 A175297
Adjacent sequences: A007428 A007429 A007430 * A007432 A007433 A007434
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KEYWORD
| nonn,nice,mult
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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