The counting functions for cyclic, abelian and nilpotent numbers in a Beatty sequence obey the same asymptotic formulas as the unrestricted counts, multiplied by the constant 1/α.
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Numbers in a Beatty sequence which are orders only of cyclic, abelian or nilpotent groups
The counting functions for cyclic, abelian and nilpotent numbers in a Beatty sequence obey the same asymptotic formulas as the unrestricted counts, multiplied by the constant 1/α.