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A formula on Stirling numbers of the second kind $S(n, k)$ is proved. As acorollary, for odd $n$ and even $k$, it is shown that $k!S(n, k)$ is a positivemultiple of the greatest common divisor of $j!S(n, j)$ for $k+1\leq j\leq n$.Also, as an application to algebraic topology, some isomorphisms of unstable$K^1$-groups of stunted complex projective spaces are deduced.

A formula on Stirling numbers of the second kind and its application to the unstable $K$-theory of stunted complex projective spaces