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We extend this by showing that, without condition on t, all but a zero-density set of integers n satisfy M(t,n) = Floor[ n / log(t) - 1/2 ]. Using a metric result of Schmidt, we show that almost all t have asymptotically log(t) log(x)/12 exceptional n<x. 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In a recent article in the Monthly, Nathanson proved that if log(t) is rational, then for all but finitely many positive integers n one has M(t,n) = Floor[ n / log(t) - 1/2 ]. We extend this by showing that, without condition on t, all but a zero-density set of integers n satisfy M(t,n) = Floor[ n / log(t) - 1/2 ]. Using a metric result of Schmidt, we show that almost all t have asymptotically log(t) log(x)/12 exceptional n<x. 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