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A038996 Sublattices of index n in generic 9-dimensional lattice. 12
1, 511, 9841, 174251, 488281, 5028751, 6725601, 50955971, 72636421, 249511591, 235794769, 1714804091, 883708281, 3436782111, 4805173321, 13910980083, 7411742281, 37117211131, 17927094321, 85083452531, 66186639441, 120491126959, 81870575521, 501457710611, 198682027181 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

M. Baake, "Solution of coincidence problem...", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sublattices

FORMULA

f(Q, n)=Sum d*f(Q-1, d), d|n; here Q=9.

Multiplicative with a(p^e) = Product_{k=1..8} (p^(e+k)-1)/(p^k-1).

Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k). - R. J. Mathar, Apr 01 2011

MATHEMATICA

f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 8}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

CROSSREFS

Cf. A001001, A038991, A038992, A038993, A038994, A038995, A038997, A038998, A038999.

Sequence in context: A075948 A011559 A160953 * A068025 A075943 A075944

Adjacent sequences:  A038993 A038994 A038995 * A038997 A038998 A038999

KEYWORD

nonn,mult

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Offset changed to 1 by R. J. Mathar, Apr 01 2011

More terms from Amiram Eldar, Aug 29 2019

STATUS

approved

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Last modified October 23 09:28 EDT 2019. Contains 328345 sequences. (Running on oeis4.)