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
FORMULA
f(Q, n) = Sum_{d|n} d*f(Q-1, d); here Q=8.
Multiplicative with a(p^e) = Product_{k=1..7} (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^8, where c = Pi^20*zeta(3)*zeta(5)*zeta(7)/43401015000 = 0.285716... . - Amiram Eldar, Oct 19 2022
MATHEMATICA
f[p_, e_] := Product[(p^(e + k) - 1)/(p^k - 1), {k, 1, 7}]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
EXTENSIONS
Offset set to 1 by R. J. Mathar, Mar 01 2011
More terms from Amiram Eldar, Aug 29 2019
STATUS
approved