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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.
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.
Sequence in context: A204736 A160674 A034817 * A203556 A038993 A068022
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 19 07:31 EDT 2024. Contains 370955 sequences. (Running on oeis4.)