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    The Multiply Perfect Numbers Page

    dataset website

    • Achim Flammenkamp
    • Richard Schroeppel

    Let $\sigma(n)$ be the number theoretic function which denotes the sum of all divisors of a natural number $n$. If $\sigma(n)$ is an integral multiply of $n$, then $n$ is denoted as a multiply perfect number or $k$-fold perfect number. As of the end of 2022 there are 5932 multiply perfect numbers known.

    Updated: June 6, 2025

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