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arXiv · 1803.00324

Primitive weird numbers having more than three distinct prime factors

Gianluca Amato·Maximilian F. Hasler·Giuseppe Melfi·Maurizio Parton
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Abstract

In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a given number of distinct prime factors are presented. These algorithms yield primitive weird numbers of the form $mp_1\dots p_k$ for a suitable deficient positive integer $m$ and primes $p_1,\dots,p_k$ and generalize a recent technique developed for generating primitive weird numbers of the form $2^np_1p_2$. The same techniques can be used to search for odd weird numbers, whose existence is still an open question.

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Gianluca Amato, Maximilian F. Hasler, Giuseppe Melfi, Maurizio Parton. 2018-03-01. Primitive weird numbers having more than three distinct prime factors. https://arxiv.org/abs/1803.00324

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