Due to the input current dead zones, the buck power factor correction converter has to set a fixed output voltage for a tradeoff between the total harmonic distortion (THD <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${_\mathit{i}}$</tex-math></inline-formula> ) and efficiency. Thus, many converter-cell integrated buck-type converters have been proposed to eliminate the dead zones, which unfortunately deteriorate efficiency due to the extra components.This article proposes a group of bridgeless buck-type integrated topologies. Then, a dead-zone-free bridgeless buck-type topology with a wide output voltage range is targeted for further study. The studied converter operates in the buck+flyback mode and can automatically change to flyback mode when the dead zones occur, which only requires a simple control. Moreover, an integrated transformer based on an E-E core is investigated to reduce cost and volume. The bridgeless operation modes are introduced, followed by the PF and THD <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${_\mathit{i}}$</tex-math></inline-formula> analysis to optimize its performance. Prototypes are built and tested, which confirm the effectiveness of the converter and the integrated magnetic.