|
|
MATHEMATICA
|
b1[m_, n_] := Sum[EulerPhi[c]*EulerPhi[d]*2^(m*n/LCM[c, d]), {c, Divisors[ m]}, {d, Divisors[n]}]/(4*m*n);
b2a[m_, n_] := If[OddQ[m], 2^((m+1)*n/2)/(4n), (2^(m*n/2) + 2^((m+2)*n/2))/(8n)];
b2b[m_, n_] := DivisorSum[n, If[# >= 2, EulerPhi[#]*2^((m*n)/#), 0]&]/(4n);
b2c[m_, n_] := If[OddQ[m], Sum[If[OddQ[n/GCD[j, n]], 2^((m+1)*GCD[j, n]/2) - 2^(m*GCD[j, n]), 0], {j, 1, n-1}]/(4*n), Sum[If[OddQ[n/GCD[j, n]], 2^(m*GCD[j, n]/2) + 2^((m+2)*GCD[j, n]/2) - 2^(m*GCD[j, n]+1), 0], {j, 1, n-1}]/(8n)];
b2[m_, n_] := b2a[m, n] + b2b[m, n] + b2c[m, n];
b3[m_, n_] := b2[n, m]; b4oo[m_, n_] := 2^((m*n - 3)/2);
b4eo[m_, n_] := 3*2^(m*n/2 - 3); b4ee[m_, n_] := 7*2^(m*n/2 - 4);
a[m_, n_] := Module[{b}, If[OddQ[m], If[OddQ[n], b = b4oo[m, n], b = b4eo[m, n]], If[OddQ[n], b = b4eo[m, n], b = b4ee[m, n]]]; b += b1[m, n] + b2[m, n] + b3[m, n]; Return[b]];
a[m_] := a[m, 2];
|
