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 A160889 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 4. 7
 1, 7, 13, 28, 31, 91, 57, 112, 117, 217, 133, 364, 183, 399, 403, 448, 307, 819, 381, 868, 741, 931, 553, 1456, 775, 1281, 1053, 1596, 871, 2821, 993, 1792, 1729, 2149, 1767, 3276, 1407, 2667, 2379, 3472, 1723, 5187, 1893, 3724, 3627, 3871, 2257, 5824, 2793 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Dirichlet convolution of A000290 and the series of absolute values of A063441. - R. J. Mathar, Jun 20 2011 a(n) is the number of lattices L in Z^3 such that the quotient group Z^3 / L is C_nm x C_m x C_m  (and also C_nm x C_nm x C_m), for every m>=1. - Álvar Ibeas, Oct 30 2015 REFERENCES J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. See p. 134. LINKS Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000 FORMULA Moebius transform of A064969. Multiplicative with a(p^e) = (p^2+p+1)*p^(2*e-2). - Vladeta Jovovic, Nov 21 2009 a(n) = J_3(n)/J_1(n)=J_3(n)/phi(n)=A059376(n)/A000010(n), where J_k is the k-th Jordan Totient Function. - Enrique Pérez Herrero, Aug 22 2010 Dirichlet g.f.: zeta(s-2)*product_{primes p} (1+p^(1-s)+p^(-s)). - R. J. Mathar, Jun 20 2011 From Álvar Ibeas, Oct 30 2015: (Start) a(n) = A254981(n^2). For squarefree n, a(n) = A000203(n^2). a(n) = Sum_{d|n, n/d squarefree} d^2 * A000203(n/d). (End) Sum_{k=1..n} a(k) ~ c * n^3 / 3, where c = A330595 = Product_{primes p} (1 + 1/p^2 + 1/p^3) = 1.748932997843245303033906997685114802259883493595480897273662144... - Vaclav Kotesovec, Dec 18 2019 Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + p^2/((p^2-1) * (p^2 + p + 1))) = 1.400940662893945919882073637564538872630336562726971915578687405304250550... - Vaclav Kotesovec, Sep 19 2020 EXAMPLE There are 35 = A160870(4,3) lattices of volume 4 in Z^3. Among them, 28 give the quotient group C_4 and 7 give the quotient group C_2 x C_2. Hence, a(4) = 28 and a(2) = 7. There are 2667 = A160870(32,3) lattices of volume 32 in Z^3. Among them, a(32) = 1792 give the quotient group C_32 (m=1); a(4) = 28 give C_8 x C_2 x C_2 (m=2); a(2) = 7 give C_4 x C_4 x C_2 (m=2). MATHEMATICA A160889[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(4-1)/EulerPhi[n]&] (* Enrique Pérez Herrero, Aug 22 2010 *) PROG (PARI) vector(100, n, sumdiv(n^2, d, if (ispower(d, 3), moebius(sqrtnint(d, 3))*sigma(n^2/d), 0))) \\ Altug Alkan, Oct 30 2015 CROSSREFS Sequence in context: A146718 A146646 A096194 * A283650 A045463 A082221 Adjacent sequences:  A160886 A160887 A160888 * A160890 A160891 A160892 KEYWORD nonn,mult,changed AUTHOR N. J. A. Sloane, Nov 19 2009 EXTENSIONS Definition corrected by Vladeta Jovovic, Nov 21 2009 Typo in Mathematica program and formula fixed by Enrique Pérez Herrero, Oct 19 2010 STATUS approved

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Last modified September 29 07:08 EDT 2020. Contains 337425 sequences. (Running on oeis4.)