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September 25, 2025Journal of Mathematics ResearchOpen Access

On the Smarandache Function Equation ∑_(d|n)S(d)=n+l

Kyasia A. Avery Jayden I. Brown Melinda E. Combs Alyssa M. Edgerton Soniya M. Fountain D. Holman Meeya H. Johnson-Williams D. Lynch Za’kiya M. Toomer-Sanders Yuan Li

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Key Points

The equation reveals that for each natural number n, a relationship exists between its divisors and the smarandache function.
Special emphasis is placed on solving $∑_{d|n}S(d)=n+l$ where l is non-negative, showing its implications for natural numbers.
The investigation into the structure of $S(n)$ deepens the understanding of how divisor functions relate to n and l.
Findings suggest further exploration of the smarandache function may uncover more patterns relevant to number theory.

Implication

This research explores solutions to the diophantine equation involving the smarandache function, indicating unique properties in natural numbers.

Abstract

Let $S(n)$ be the Smarandache function, we solve Diophantine equation ∑d|nS(d)=n+l, l≥ 0 and n∈ N in this paper.

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Cite This Study

Avery et al. (2025) studied this question.

synapsesocial.com/papers/68d90a0641e1c178a14f63f5 https://doi.org/10.5539/jmr.v17n3p19

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