OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, pp. 274-276.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A_1*B_1*n + A_2*B_2*n^(1/2) + A_3*B_3*n^(1/3) + O(n^(50/199+eps)), where A_k = Product_{m>=1, m!=k} zeta(m/k) and B_k = Product_{r>=1, m>=2} zeta(r*m^2/k) (Finch, 2003). - Amiram Eldar, Jan 31 2024
MATHEMATICA
With[{emax = 7}, f[e_] := f[e] = Coefficient[Series[Product[1/(1 - x^(j*k^2)), {k, 1, Floor[Sqrt[emax]] + 1}, {j, 1, Floor[emax/k^2] + 1}], {x, 0, emax}], x, e]; a[1] = 1; a[n_] := Times @@ f /@ FactorInteger[n][[;; , 2]]; Accumulate@ Array[a, 2^emax]] (* Amiram Eldar, Jan 31 2024, using code by Vaclav Kotesovec at A004101 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, Jul 07 2008
STATUS
approved