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 A160953 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 10. 3
 1, 511, 9841, 130816, 488281, 5028751, 6725601, 33488896, 64566801, 249511591, 235794769, 1287360256, 883708281, 3436782111, 4805173321, 8573157376, 7411742281, 32993635311, 17927094321, 63874967296, 66186639441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of lattices L in Z^9 such that the quotient group Z^9 / L is C_n. - Álvar Ibeas, Nov 03 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 Enrique Pérez Herrero, Mathematica Package: Jordan Totient Function. FORMULA a(n) = J_9(n)/phi(n) = A069094(n)/A000010(n). From Álvar Ibeas, Nov 03 2015: (Start) Multiplicative with a(p^e) = p^(8e-8) * (p^9-1) / (p-1). For squarefree n, a(n) = A000203(n^8). (End) MAPLE A160953 := proc(n)     add(numtheory[mobius](n/d)*d^9, d=numtheory[divisors](n)) ;     %/numtheory[phi](n) ; end proc: for n from 1 to 5000 do     printf("%d %d\n", n, A160953(n)) ; end do: # R. J. Mathar, Mar 14 2016 MATHEMATICA JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/#]&]/; (n>0)&&IntegerQ[n]; A160953[n_]:=JordanTotient[n, 9]/JordanTotient[n]; PROG (PARI) vector(100, n, sumdiv(n^8, d, if(ispower(d, 9), moebius(sqrtnint(d, 9))*sigma(n^8/d), 0))) \\ Altug Alkan, Nov 05 2015 (PARI) a(n) = {f = factor(n); for (i=1, #f~, p = f[i, 1]; f[i, 1] = p^(8*f[i, 2]-8)*(p^9-1)/(p-1); f[i, 2] = 1; ); factorback(f); } \\ Michel Marcus, Nov 12 2015 CROSSREFS Sequence in context: A204739 A075948 A011559 * A038996 A068025 A075943 Adjacent sequences:  A160950 A160951 A160952 * A160954 A160955 A160956 KEYWORD nonn,mult AUTHOR N. J. A. Sloane, Nov 19 2009 EXTENSIONS Definition corrected by Enrique Pérez Herrero, Oct 30 2010 STATUS approved

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