In this article, novel packaged wideband highly selective filtering power dividers (FPDs) with arbitrary phase shifts and power dividing ratios using multilayer stacked stripline are presented, for the first time. In the proposal, the arbitrary phase shift $\Delta \Phi $ and power dividing ratio $k^{2}$ are mainly attained by developing a novel topology consisting of a looped double-coupled line (LDCL)-based power dividing section, a pair of shorted stubs and a delay line. And, it requires no additional output transformers to terminals under arbitrary power dividing ratios. In addition, a co-shared structure composed of a transmission line and an open-circuit stepped impendence stub is inserted in front of the proposed LDCL, which can enhance the flexibility of overall impedance requirement and bring more transmission poles (TPs) and a pair of transmission zeros (TZs), realizing a wide and high-selective filtering bandwidth and enhanced isolation. A comprehensive analysis is carried out to guide the proposed FPDs design in detail. For verification, two design prototypes are implemented in self-packaged forms using the multilayer stacked stripline printed circuit board (PCB) technology. Prototype I is a FPD with 84% 3-dB FBW, phase shift $\Delta \Phi$ $=$ 45 $^{\circ}$ , and power dividing ratio $k^{2}$ $=$ 1, while prototype II is an FPD with 72% 3-dB FBW, phase shift $\Delta \Phi$ $=$ 90 $^{\circ}$ , and power dividing ratio $k^{2}$ $=$ 6. Simulated and measured results are provided with satisfying agreement among them.