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arXiv · 1906.10001

On a problem of De Koninck

Tomohiro Yamada
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Abstract

Let $\sigma(n)$ and $\gamma(n)$ denote the sum of divisors and the product of distinct prime divisors of $n$ respectively. We shall show that, if $n\neq 1, 1782$ and $\sigma(n)=(\gamma(n))^2$, then there exist odd (not necessarily distinct) primes $p, p^\prime$ and (not necessarily odd) distinct primes $q_i (i=1, 2, \ldots, k)$ such that $p, p^\prime\mid\mid n$, $q_i^2\mid\mid n (i=1, 2, \ldots, k)$ and $q_1\mid \sigma(p^2), q_{i+1}\mid\sigma(q_i^2) (1\leq i\leq k-1), p^\prime \mid\sigma(q_k^2)$.

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Tomohiro Yamada. 2019-06-24. On a problem of De Koninck. https://doi.org/10.2140/moscow.2021.10.249

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