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A064803
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Number of subgroups of the group C_n X C_n X C_n (where C_n is the cyclic group of order n).
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4
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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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
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MAPLE
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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 ;
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Oct 21 2001
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EXTENSIONS
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STATUS
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approved
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