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 A160895 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7. 7
 1, 63, 364, 2016, 3906, 22932, 19608, 64512, 88452, 246078, 177156, 733824, 402234, 1235304, 1421784, 2064384, 1508598, 5572476, 2613660, 7874496, 7137312, 11160828, 6728904, 23482368, 12206250, 25340742, 21493836, 39529728, 21243690, 89572392 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of lattices L in Z^6 such that the quotient group Z^6 / L is C_nm x (C_m)^5 (and also (C_nm)^5 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 a(n) = J_6(n)/J_1(n)=J_6(n)/phi(n)=A069091(n)/A000010(n), where J_k is the k-th Jordan Totient Function. - Enrique Pérez Herrero, Oct 20 2010 Multiplicative with a(p^e) = p^(5e-5)*(1+p+p^2+p^3+p^4+p^5). - R. J. Mathar, Jul 10 2011 For squarefree n, a(n) = A000203(n^5). - Álvar Ibeas, Oct 30 2015 MAPLE A160895 := proc(n) a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; a := a*p^(5*e-5)*(1+p+p^2+p^3+p^4+p^5) ; end do; a; end proc: # R. J. Mathar, Jul 10 2011 MATHEMATICA A160895[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(7-1)/EulerPhi[n]&] (* Enrique Pérez Herrero, Oct 20 2010 *) PROG (PARI) vector(50, n, sumdiv(n^5, d, if(ispower(d, 6), moebius(sqrtnint(d, 6))*sigma(n^5/d), 0))) \\ Altug Alkan, Oct 30 2014 (PARI) a(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; f[i, 1] = p^(5*f[i, 2]-5)*(1+p+p^2+p^3+p^4+p^5); 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, A160897, A160908, A160960, A160972, A161010, A161025, A161139, A161167, A161213, A065958, A065959, A065960. - Enrique Pérez Herrero, Oct 20 2010 Sequence in context: A204736 A160674 A034817 * A203556 A038993 A068022 Adjacent sequences:  A160892 A160893 A160894 * A160896 A160897 A160898 KEYWORD nonn,mult,changed AUTHOR N. J. A. Sloane, Nov 19 2009 EXTENSIONS Definition corrected by Enrique Pérez Herrero, Oct 20 2010 STATUS approved

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