Finiteness conjecture for strongly pseudoperfect μ-Sondow numbers

For an integer μ\mu, a μ\mu-Sondow number is a positive integer nn such that

μn+pn1pN,\frac{\mu}{n}+\sum_{p\mid n}\frac{1}{p}\in\mathbb{N},

where the sum is over the prime divisors pp of nn. A strongly pseudoperfect number is understood in the sense defined in the paper. Finiteness conjecture for strongly pseudoperfect μ\mu-Sondow numbers. For every integer μ\mu, only finitely many μ\mu-Sondow numbers are strongly pseudoperfect. The source presents this as a conjecture in the context of the rarity of fixed-μ\mu μ\mu-Sondow numbers and gives no resolution status.

Sources & referencesView supporting material

Primary source

Tim McCormack and Joshua Zelinsky, “Weighted Versions of the Arithmetic-Mean-Geometric Mean Inequality and Zaremba's Function”, arXiv:2312.11661 (2024).

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