x^(\[Omega][n m] - \[Omega][m]) == DivisorSum[(x^\[Omega][n/d] (1 - t))^ \[CapitalOmega][d], {d, GCD[n, m]}] /; Element[x, Reals] && (\[Omega][k] == r /; k == Product[Prime[j]^Subscript[n, j], {j, 1, r}]) && (\[CapitalOmega][k] == Sum[Subscript[n, j], {j, 1, r}] /; k == Product[Prime[j]^Subscript[n, j], {j, 1, r}])

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2001-10-29