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A160895 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 7. 5
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

LINKS

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Jin Ho Kwak and Jaeun 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.

Index to Jordan function ratios J_k/J_1.

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

From Amiram Eldar, Nov 08 2022: (Start)

Sum_{k=1..n} a(k) ~ c * n^6, where c = (1/6) * Product_{p prime} (1 + (p^5-1)/((p-1)*p^6)) = 0.3203646372... .

Sum_{k>=1} 1/a(k) = zeta(5)*zeta(6) * Product_{p prime} (1 - 2/p^6 + 1/p^11) = 1.0195114923... . (End)

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 *)

f[p_, e_] := p^(5*e - 5) * (p^6-1) / (p-1); ; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30] (* Amiram Eldar, Nov 08 2022 *)

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

Column 6 of A263950.

Cf. A000010, A000203, A013663, A013664, A069091.

Sequence in context: A204736 A160674 A034817 * A203556 A038993 A068022

Adjacent sequences: A160892 A160893 A160894 * A160896 A160897 A160898

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane, Nov 19 2009

EXTENSIONS

Definition corrected by Enrique Pérez Herrero, Oct 20 2010

STATUS

approved

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Last modified March 24 04:28 EDT 2023. Contains 361454 sequences. (Running on oeis4.)