Dandapat–Hunsucker–Pomerance (1975): $\sigma(p^k)=2m^2$ and $\sigma(m^2)=p^k$ are incompatible

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Dandapat–Hunsucker–Pomerance (1975): $\sigma(p^k)=2m^2$ and $\sigma(m^2)=p^k$ are incompatible · Prove2Me