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A063445
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Moebius transform of f[x]=EulerPhi[x^2] function(=A002618).
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0
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1, 1, 5, 6, 19, 5, 41, 24, 48, 19, 109, 30, 155, 41, 95, 96, 271, 48, 341, 114, 205, 109, 505, 120, 480, 155, 432, 246, 811, 95, 929, 384, 545, 271, 779, 288, 1331, 341, 775, 456, 1639, 205, 1805, 654, 912, 505, 2161, 480, 2016, 480, 1355, 930, 2755, 432
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Same as Moebius transform of g[x]=x*EulerPhi[x] - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 05 2002
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FORMULA
| a(n)=Sum{Phi[d^2]*mu[n/d]}, d divides n
Multiplicative with a(p) = p^2-p-1 and a(p^e) = p^(2*e)-p^(2*e-1)-p^(2*e-2)+p^(2*e-3), e>1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 29 2001
Dirichlet g.f. zeta(s-2)/(zeta(s)*zeta(s-1)). - R. J. Mathar, Feb 09 2011
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EXAMPLE
| n=20,divisors={1,2,4,5,10,20},Phi[d^2]={1,2,8,20,40,160}, mu[20/d]={0,1,-1,0,-1,1}, a(20)=0+2-8+0-40+160=114
a(20)=a(4)*a(5)=(16-8-4+2)*(25-5-1)=6*19=114.
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PROG
| (PARI) a(n)=if(n<1, 0, sumdiv(n, d, d*eulerphi(d)*moebius(n/d)))
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CROSSREFS
| Cf. A057660, A000010, A002618.
Sequence in context: A180134 A192727 A056519 * A031448 A163772 A056509
Adjacent sequences: A063442 A063443 A063444 * A063446 A063447 A063448
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KEYWORD
| nonn,mult
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 24 2001
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