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A038998
Sublattices of index n in generic 11-dimensional lattice.
11
1, 2047, 88573, 2794155, 12207031, 181308931, 329554457, 3269560515, 5883904390, 24987792457, 28531167061, 247486690815, 149346699503, 674597973479, 1081213356763, 3571013994483, 2141993519227, 12044352286330, 6471681049901, 34108336703805, 29189626919861
OFFSET
1,2
REFERENCES
Michael Baake, "Solution of the coincidence problem in dimensions", in R. V. Moody, ed., Math. of Long-Range Aperiodic Order, Kluwer 1997, pp. 9-44.
FORMULA
f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=11.
Multiplicative with a(p^e) = Product_{k=1..10} (p^(e+k)-1)/(p^k-1).
Dirichlet g.f.: Product_{k=0..Q-1} zeta(s-k).
Sum_{k=1..n} a(k) ~ c * n^11, where c = Pi^30*zeta(3)*zeta(5)*zeta(7)*zeta(9)*zeta(11)/4962689060175000 = 0.208520... . - Amiram Eldar, Oct 19 2022
MATHEMATICA
f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 10}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)
KEYWORD
nonn,mult
EXTENSIONS
Offset set to 1 by R. J. Mathar, Apr 01 2011
More terms from Amiram Eldar, Aug 29 2019
STATUS
approved