Darrell Cox

most citedCollatz Cycles and

3 n + c

Cycles

1 citations · 4 across the 5 of their papers we have counts for

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4 papers · 1 filter

math.GM2021★ 1 cited

Measuring Abundance with Abundancy Index

Kalpok Guha, Sourangshu Ghosh

A positive integer $n$ is called perfect if $σ (n) = 2 n$ , where $σ (n)$ denote the sum of divisors of $n$ . In this paper we study the ratio $\frac{σ ( n )}{n}$ . We define the function Ab…

math.GM2021★ 1 cited

Collatz Cycles and $3 n + c$ Cycles

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

Halbeisen and Hungerbuhler determined optimal bounds for the length of rational Collatz cycles. Their methods are extended to $3 n + c$ cycles. Another sequence having properties simi…

math.GM2020★ 1 cited

Bounds of the Mertens Function

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

In this paper, we derive new properties of the Mertens function and discuss a likely upper bound of the absolute value of the Mertens function $lo g x! > ∣ M (x) ∣$ when $x > 1$ .…

math.GM2020

Sequences and Polynomial Congruence

Darrell Cox, Sourangshu Ghosh, Eldar Sultanow

In this paper, we shall find a new connection between $n$ th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discu…

Measuring Abundance with Abundancy Index

Collatz Cycles and 3n+c Cycles

Bounds of the Mertens Function

Sequences and Polynomial Congruence

Collatz Cycles and $3 n + c$ Cycles