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 A160893 a(n) = Sum_{d|n} Möbius(n/d)*d^5/phi(n). 4
 1, 31, 121, 496, 781, 3751, 2801, 7936, 9801, 24211, 16105, 60016, 30941, 86831, 94501, 126976, 88741, 303831, 137561, 387376, 338921, 499255, 292561, 960256, 488125, 959171, 793881, 1389296, 732541, 2929531, 954305, 2031616, 1948705 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of lattices L in Z^5 such that the quotient group Z^5 / L is C_nm x (C_m)^4 (and also (C_nm)^4 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_5(n)/J_1(n) = J_5(n)/phi(n) = A059378(n)/A000010(n), where J_k is the k-th Jordan Totient Function. - Enrique Pérez Herrero, Oct 19 2010 Multiplicative with a(p^e) = p^(4e-4)*(1 + p+ p^2 + p^3 + p^4). - R. J. Mathar, Jul 10 2011 For squarefree n, a(n) = A000203(n^4). - Álvar Ibeas, Oct 30 2015 MAPLE A160893 := proc(n) a := 1 ; for f in ifactors(n)[2] do p := op(1, f) ; e := op(2, f) ; a := a*p^(4*e-4)*(1+p+p^2+p^3+p^4) ; end do; a; end proc: # R. J. Mathar, Jul 10 2011 MATHEMATICA A160893[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(6-1)/EulerPhi[n]&] (* Enrique Pérez Herrero, Oct 19 2010 *) PROG (PARI) a(n) = sumdiv(n, d, moebius(n/d)*d^5/eulerphi(n)); \\ Michel Marcus, Feb 15 2015 CROSSREFS Sequence in context: A256650 A131550 A158558 * A202994 A038992 A068021 Adjacent sequences:  A160890 A160891 A160892 * A160894 A160895 A160896 KEYWORD nonn,mult AUTHOR N. J. A. Sloane, Nov 19 2009 EXTENSIONS Definition corrected by Enrique Pérez Herrero, Oct 19 2010 STATUS approved

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Last modified February 20 16:42 EST 2020. Contains 332080 sequences. (Running on oeis4.)