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 A160897 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8. 8
 1, 127, 1093, 8128, 19531, 138811, 137257, 520192, 796797, 2480437, 1948717, 8883904, 5229043, 17431639, 21347383, 33292288, 25646167, 101193219, 49659541, 158747968, 150021901, 247487059, 154764793, 568569856, 305171875, 664088461 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of lattices L in Z^7 such that the quotient group Z^7 / L is C_n. - 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 a(n) = J_7(n)/J_1(n)=J_7(n)/phi(n)=A069092(n)/A000010(n), where J_k is the k-th Jordan Totient Function. - Enrique Pérez Herrero, Oct 27 2010 From Álvar Ibeas, Oct 30 2015: (Start) Multiplicative with a(p^e) = p^(6e-6) * (p^7-1) / (p-1). For squarefree n, a(n) = A000203(n^6). (End) MATHEMATICA A160897[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(8 - 1)/EulerPhi[n] &] (* Enrique Pérez Herrero, Oct 27 2010 *) PROG (PARI) vector(30, n, sumdiv(n^6, d, if(ispower(d, 7), moebius(sqrtnint(d, 7))*sigma(n^6/d), 0))) \\ Altug Alkan, Oct 30 2015 (PARI) a(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; f[i, 1] = p^(6*f[i, 2]-6)*(1+p+p^2+p^3+p^4+p^5+p^6); f[i, 2] = 1; ); factorback(f); } \\ Michel Marcus, Nov 12 2015 CROSSREFS Cf. A000010, A007434, A059376, A059377, A059378, A069091, A069092, A069093, A069094, A069095, A001615, A160889, A160891, A160893, A160895, A160908, A160960, A160972, A161010, A161025, A161139, A161167, A161213, A065958, A065959, A065960. - Enrique Pérez Herrero, Oct 27 2010 Sequence in context: A196658 A077361 A225148 * A038994 A068023 A194257 Adjacent sequences:  A160894 A160895 A160896 * A160898 A160899 A160900 KEYWORD nonn,mult,changed AUTHOR N. J. A. Sloane, Nov 19 2009 EXTENSIONS Definition corrected by Enrique Pérez Herrero, Oct 27 2010 STATUS approved

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