Marco Mantovanelli

collaborators

7 papers

math.NT2026

Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite Numbers

Marco Mantovanelli

Let $d (n)$ be the divisor function and let $H < H^{'}$ be consecutive highly composite numbers. We study directed unit moves between their prime-exponent vectors under the hard ceiling…

math.GM2026

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers

Marco Mantovanelli

For an odd perfect number $N$ , write $q = min {p : p ∣ N}$ for its smallest prime divisor. This paper proves a certified branch-closure theorem for the five minimal-prime branches…

math.CO2026

A Dyadic Frequency Law for a Perturbed Hofstadter $Q$ -Recursion

Marco Mantovanelli

We study the perturbed Hofstadter $Q$ -recursion $Q (1) = Q (2) = 1, Q (n) = Q (n - Q (n - 1)) + Q (n - Q (n - 2)) + (- 1)^{n} (n \geq 3) .$ CloÃ®tre proved that the recursion is globally well-def…

math.CO2026

Certified Return-Word Induction for a Perturbed Hofstadter Recursion

Marco Mantovanelli

We study the parity-perturbed Hofstadter recursion $Q (1) = Q (2) = 1, Q (n) = Q (n - Q (n - 1)) + Q (n - Q (n - 2)) + (- 1)^{n} .$ We prove that it is well-defined for every $n \geq 1$ by a computer-a…

math.CO2026

Averaged Extensions of Golomb's Triangular Recursion: Critical Invariance and Supercritical Constraints

Marco Mantovanelli

For an integer $m \geq 1$ and a parameter $I^\pm > 0$ , consider the nested recursion $$ Q_{Î±,m}(n)=1+\left\lfloor \fracÎ±{m}\sum_{j=1}^m Q_{Î±,m}\!\left(n-Q_{Î±,m}(n-j)\right)\right\rflo…

math.NT2026

The Subtractive Divisor Orbit: Unconditional Bounds, Parity Constraints, and a Conditional Framework

Marco Mantovanelli

Let $I ¨ (n)$ denote the number of positive divisors of $n$ . Starting from $n_{0} = x$ , consider the orbit $n_{j + 1} = n_{j} - I ¨ (n_{j})$ , and let $a (x)$ be its hitting time of zero. Although the…

Prime-Exponent Transition Geometry and Divisor Barriers Between Consecutive Highly Composite Numbers

Certified Minimal-Prime Branch Closures for Odd Perfect Numbers

A Dyadic Frequency Law for a Perturbed Hofstadter Q-Recursion

Certified Return-Word Induction for a Perturbed Hofstadter Recursion

Averaged Extensions of Golomb's Triangular Recursion: Critical Invariance and Supercritical Constraints

The Subtractive Divisor Orbit: Unconditional Bounds, Parity Constraints, and a Conditional Framework

A Dyadic Frequency Law for a Perturbed Hofstadter $Q$ -Recursion