August 1 to November 15, 2016 period was characterized by the presence of Corotating Interaction Regions (CIRs) and a few weak Coronal Mass Ejections (CMEs) in the heliosphere. In this study we show recurrent energetic electron and proton enhancements observed near Earth (1 AU) and Mars (1.43-1.38 AU) during this period. The observations near Earth are using data from instruments aboard ACE, SOHO, and SDO whereas those near Mars are by the SEP, SWIA, and MAG instruments aboard MAVEN. During this period, the energetic electron fluxes observed near Earth and Mars showed prominent periodic enhancements over four solar rotations, with major periodicities of ∼27 days and ∼13 days. Periodic radar blackout/weakening of radar signals at Mars are observed by MARSIS/MEX, associated with these solar energetic electron enhancements. During this period, a weak CME and a High Speed Stream (HSS)-related interplanetary shock could interact with the CIR and enhance energetic proton fluxes near 1.43-1.38 AU, and as a result, ∼27 day periodicity in proton fluxes is significantly diminished at 1.43-1.38 AU. These events also cause unexpected impact on the Martian topside ionosphere, such as topside ionospheric depletion and compression observed by LPW and NGIMS onboard MAVEN. These observations are unique not only because of the recurring nature of electron enhancements seen at two vantage points, but also because they reveal unexpected impact of the weak CME and interplanetary shock on the Martian ionosphere, which provide new insight into the impact of CME-HSS interactions on Martian plasma environment.