A123030 Partial sums of A038538.

1, 2, 3, 5, 6, 7, 8, 11, 13, 14, 15, 17, 18, 19, 20, 26, 27, 29, 30, 32, 33, 34, 35, 38, 40, 41, 44, 46, 47, 48, 49, 57, 58, 59, 60, 64, 65, 66, 67, 70, 71, 72, 73, 75, 77, 78, 79, 85, 87, 89, 90, 92, 93, 96, 97, 100, 101, 102, 103, 105, 106, 107, 109, 122, 123, 124, 125, 127, 128

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

Cf. A038538, A244285 (A_1*B_1).

Sequence in context: A116545 A140661 A063966 * A284836 A267300 A063752

Adjacent sequences: A123027 A123028 A123029 * A123031 A123032 A123033

Keyword

nonn

Author

Jonathan Vos Post, Jul 07 2008

Status

approved