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A160897
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a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 8.
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5
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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
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OFFSET
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1,2
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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Enrique Pérez Herrero and Robert Israel, Table of n, a(n) for n = 1..10000 (n = 1..5000 from Enrique Pérez Herrero)
Index to Jordan function ratios J_k/J_1
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FORMULA
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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)
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MAPLE
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A160897 := proc(n)
add(numtheory[mobius](n/d)*d^7, d=numtheory[divisors](n)) ;
%/numtheory[phi](n) ;
end proc:
for n from 1 to 5000 do
printf("%d %d\n", n, A160897(n)) ;
end do: # R. J. Mathar, Mar 14 2016
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MATHEMATICA
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A160897[n_]:=DivisorSum[n, MoebiusMu[n/# ]*#^(8 - 1)/EulerPhi[n] &] (* Enrique Pérez Herrero, Oct 27 2010 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A196658 A077361 A225148 * A038994 A068023 A194257
Adjacent sequences: A160894 A160895 A160896 * A160898 A160899 A160900
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KEYWORD
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nonn,mult
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AUTHOR
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N. J. A. Sloane, Nov 19 2009
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EXTENSIONS
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Definition corrected by Enrique Pérez Herrero, Oct 27 2010
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STATUS
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approved
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