  Let $a_1,a_2,\dots,a_k$ be positive integers with
$\gcd(a_1,a_2,\dots,a_k)=1$. Frobenius number is the largest positive integer
that is NOT representable in terms of $a_1,a_2,\dots,a_k$. When $k\ge 3$, there
is no explicit formula in general, but some formulae may exist for special
sequences $a_1,a_2,\dots,a_k$, including, those forming arithmetic progressions
and their modifications. In this paper, we give formulae for the power and
weighted sum of nonrepresentable positive integers. As applications, we show
explicit expressions of these sums for $a_1,a_2,\dots,a_k$ forming arithmetic
progressions.
