Sequences

Number Theory Level 2

What number comes next in the following sequence of positive integers?

$\color{#3D99F6}{1},\color{#EC7300}{2},\color{#D61F06}{4},\color{#20A900}{8},\color{#69047E}{61},\color{#333333}{23},\color{#624F41}{46},\color{magenta}{821},\ldots$