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 A158523 Moebius transform of negate primes in factorization of n. 0
 1, -3, -4, 6, -6, 12, -8, -12, 12, 18, -12, -24, -14, 24, 24, 24, -18, -36, -20, -36, 32, 36, -24, 48, 30, 42, -36, -48, -30, -72, -32, -48, 48, 54, 48, 72, -38, 60, 56, 72, -42, -96, -44, -72, -72, 72, -48, -96, 56, -90, 72, -84, -54, 108, 72, 96, 80, 90, -60, 144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = mu(n) * A061019(n) = A008683(n) * A061019(n)  = A008683(n) * A061019(n) = A061020(n) * A007427(n) = A061020(n) * A007428(n) * A000012(n) = A007427(n) * A000012(n) * A061019(n) = A007428(n) * A000005(n) * A061019(n), where operation * denotes Dirichlet convolution. Dirichlet convolution of functions b(n), c(n) is function a(n) = b(n) * c(n) = Sum_{d|n} b(d)*c(n/d). Inverse Moebius transform of a(n) is A061019(n). a(n) = (-1)^A001222(n)*A001615(n). Multiplicative with a(p^e) = (-1)^e*(p+1)*p^(e-1). Apparently the Dirichlet inverse of A048250. [From R. J. Mathar, Jul 15 2010] LINKS FORMULA Multiplicative with a(p^e) = (-1)^e*(p+1)*p^(e-1), e>0. a(1)=1. EXAMPLE a(72)=a(2^3*3^2)=[(-1)^3*(2+1)*2^(3-1)]*[(-1)^2*(3+1)*3^(2-1)]=(-12)*12=-144. CROSSREFS Cf. A061019, A008683, A061020, A007427, A000012, A007428, A000005, A001615, A001222, A000040, A006881, A120944, A000961. Sequence in context: A185443 A275258 A230593 * A001615 A133689 A285895 Adjacent sequences:  A158520 A158521 A158522 * A158524 A158525 A158526 KEYWORD sign,mult AUTHOR Jaroslav Krizek, Mar 20 2009 STATUS approved

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