A064803 Number of subgroups of the group C_n X C_n X C_n (where C_n is the cyclic group of order n).

1, 16, 28, 129, 64, 448, 116, 802, 445, 1024, 268, 3612, 368, 1856, 1792, 4387, 616, 7120, 764, 8256, 3248, 4288, 1108, 22456, 2607, 5888, 5776, 14964, 1744, 28672, 1988, 22308, 7504, 9856, 7424, 57405, 2816, 12224, 10304, 51328, 3448, 51968, 3788, 34572, 28480, 17728, 4516, 122836, 9009, 41712

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mario Hampejs and László Tóth, On the subgroups of finite Abelian groups of rank three, Annales Univ. Sci. Budapest., Sect. Comp. 39 (2013) 111-124.

Formula

For a prime p: a(p) = 2*(p^2+p+2). - Vladeta Jovovic, Oct 22 2001

Multiplicative with a(p^e) = Sum_{j=0..2*e} (e - floor((j - 1)/2))*(2*j - floor((j - 1)/2))*p^(2*e - j)). - Amiram Eldar, Nov 29 2022

Maple

A064803 := proc(n)
    local a, f, nu, p, j ;
    a := 1 ;
    for f in ifactors(n)[2] do
        nu := op(2, f) ;
        p := op(1, f) ;
        add( (nu-floor((j-1)/2))*(2*j-floor((j-1)/2))*p^(2*nu-j), j=0..2*nu) ;
        a := a*% ;
    end do:
    a ;
end proc: # R. J. Mathar, May 11 2013

Mathematica

f[p_, e_] := Sum[(e - Floor[(j - 1)/2])*(2*j - Floor[(j - 1)/2])*p^(2*e - j), {j, 0, 2*e}]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 29 2022 *)

Crossrefs

Cf. A060648, A060724.

Sequence in context: A349418 A184031 A206259 * A220762 A353597 A246345

Adjacent sequences: A064800 A064801 A064802 * A064804 A064805 A064806

Keyword

nonn,mult

Author

Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Oct 21 2001

Extensions

More terms from Laszlo Toth, May 11 2013

Status

approved