We give a Pieri-type formula for the sum of K - k -Schur functions ∑ μ ≤ λ g μ ( k ) over a principal order ideal of the poset of k -bounded partitions under the strong Bruhat order, whose sum we denote by g ˜ λ ( k ) . As an application of this, we also give a k -rectangle factorization formula g ˜ R t ∪ λ ( k ) = g ˜ R t ( k ) g ˜ λ ( k ) where R t = ( t k + 1 - t ) , analogous to that of k -Schur functions s R t ∪ λ ( k ) = s R t ( k ) s λ ( k ) .