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A161167 a(n) = Sum_{d|n} Moebius(n/d)*d^(b-1)/phi(n) for b = 17. 3
1, 65535, 21523360, 2147450880, 38146972656, 1410533397600, 5538821761600, 70367670435840, 308836690967520, 2499961853010960, 4594972986357216, 46220358372556800, 55451384098598320, 362986684146456000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of lattices L in Z^16 such that the quotient group Z^16 / L is C_n. - Álvar Ibeas, Nov 26 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

Index to Jordan function ratios J_k/J_1

FORMULA

a(n) = J_16(n)/J_1(n) = J_16(n)/A000010(n), where J_k is the k-th Jordan Totient Function

From Álvar Ibeas, Nov 26 2015: (Start)

Multiplicative with a(p^e) = p^(15e-15) * (p^16-1) / (p-1).

For squarefree n, a(n) = A000203(n^15).

(End)

MAPLE

A161167 := proc(n)

    add(numtheory[mobius](n/d)*d^16, d=numtheory[divisors](n)) ;

    %/numtheory[phi](n) ;

end proc:

for n from 1 to 5000 do

    printf("%d %d\n", n, A161167(n)) ;

end do: # R. J. Mathar, Mar 15 2016

MATHEMATICA

A161167[n_]:=DivisorSum[n, MoebiusMu[n/#]*#^(17-1)/EulerPhi[n]&]; Array[A161167, 20]

PROG

(PARI) vector(100, n, sumdiv(n^15, d, if(ispower(d, 16), moebius(sqrtnint(d, 16))*sigma(n^15/d), 0))) \\ Altug Alkan, Nov 26 2015

CROSSREFS

Cf. A000203.

Sequence in context: A075969 A075965 A011566 * A022532 A161195 A069391

Adjacent sequences:  A161164 A161165 A161166 * A161168 A161169 A161170

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 July 5 23:36 EDT 2020. Contains 335474 sequences. (Running on oeis4.)