A038997 Number of sublattices of index n in generic 10-dimensional lattice.

1, 1023, 29524, 698027, 2441406, 30203052, 47079208, 408345795, 653757313, 2497558338, 2593742460, 20608549148, 11488207654, 48162029784, 72080070744, 222984027123, 125999618778, 668793731199, 340614792100, 1704167305962, 1389966536992, 2653398536580, 1883023236984

Offset

1,2

References

Michael Baake, "Solution of the coincidence problem in dimensions d <= 4", 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|n} d*f(Q-1, d); here Q=10.

Multiplicative with a(p^e) = Product_{k=1..9} (p^(e+k)-1)/(p^k-1).

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

Sum_{k=1..n} a(k) ~ c * n^10, where c = Pi^30*zeta(3)*zeta(5)*zeta(7)*zeta(9) / 4511535509250000 = 0.229259... . - Amiram Eldar, Oct 19 2022

Mathematica

f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 9}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

Crossrefs

Column 10 of A160870.

Cf. A001001, A038991, A038992, A038993, A038994, A038995, A038996, A038998, A038999.

Sequence in context: A223079 A011560 A160957 * A068026 A075946 A075951

Adjacent sequences: A038994 A038995 A038996 * A038998 A038999 A039000

Keyword

nonn,mult

Author

N. J. A. Sloane

Extensions

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

More terms from Amiram Eldar, Aug 29 2019

Status

approved