In this paper a modified form of perfect numbers called \((p,q)\)+ perfect numbers and their properties with examples have been discussed. Further properties of \(\sigma _{+}\) arithmetical function have been discussed and on its basis a modified form of perfect number called \((p,q)\)+ super perfect numbers have been discussed. A modified form of perfect number called \((p,0)\)-perfect and their characterization has been studied. In the end of this paper almost super perfect numbers have been introduced.
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