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A161025 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 15. 4
1, 16383, 2391484, 134209536, 1525878906, 39179682372, 113037178808, 1099444518912, 3812797945332, 24998474116998, 37974983358324, 320959957991424, 328114698808274, 1851888100411464, 3649114989636504 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) is the number of lattices L in Z^14 such that the quotient group Z^14 / L is C_n. - Álvar Ibeas, Nov 26 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_14(n)/J_1(n) where J_14 and J_1(n) = A000010(n) are Jordan functions. - R. J. Mathar, Jul 12 2011
From Álvar Ibeas, Nov 26 2015: (Start)
Multiplicative with a(p^e) = p^(13e-13) * (p^14-1) / (p-1).
For squarefree n, a(n) = A000203(n^13). (End)
From Amiram Eldar, Nov 08 2022: (Start)
Sum_{k=1..n} a(k) ~ c * n^14, where c = (1/14) * Product_{p prime} (1 + (p^13-1)/((p-1)*p^14)) = 0.1388226555... .
Sum_{k>=1} 1/a(k) = zeta(13)*zeta(14) * Product_{p prime} (1 - 2/p^14 + 1/p^27) = 1.00006146517418... . (End)
MAPLE
A161025 := proc(n)
add(numtheory[mobius](n/d)*d^14, d=numtheory[divisors](n)) ;
%/numtheory[phi](n) ;
end proc:
for n from 1 to 5000 do
printf("%d %d\n", n, A161025(n)) ;
end do: # R. J. Mathar, Mar 15 2016
MATHEMATICA
A161025[n_]:=DivisorSum[n, MoebiusMu[n/#]*#^(15-1)/EulerPhi[n]&]
f[p_, e_] := p^(13*e - 13) * (p^14-1) / (p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 20] (* Amiram Eldar, Nov 08 2022 *)
PROG
(PARI) vector(100, n, sumdiv(n^13, d, if(ispower(d, 14), moebius(sqrtnint(d, 14))*sigma(n^13/d), 0))) \\ Altug Alkan, Nov 26 2015
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^14 - 1)*f[i, 1]^(13*f[i, 2] - 13)/(f[i, 1] - 1)); } \\ Amiram Eldar, Nov 08 2022
CROSSREFS
Column 14 of A263950.
Sequence in context: A075963 A075959 A011564 * A022530 A161117 A069389
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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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)