SOME RESULTS ON ORDERED AND UNORDERED FACTORIZATION OF A POSITIVE INTEGER | ||
| Journal of Algebraic Systems | ||
| دوره 12، شماره 2، فروردین 2025، صفحه 257-267 اصل مقاله (150.91 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12044.1618 | ||
| نویسندگان | ||
| Daniel Yaqubi* 1؛ Madjid Mirzavaziri2 | ||
| 1Department of Computer science, University of Torbat e Jam, Torbat e Jam, Iran. | ||
| 2Department of Pure Mathematics, University of Ferdowsi, Mashhad, Iran. | ||
| چکیده | ||
| A well-known enumerative problem is to count the number of ways a positive integer $n$ can be factorised as $n=n_1\times n_2\times\cdots\times n_{k}$, where $n_1\geqslant n_2 \geqslant \cdots \geqslant n_{k} >1$. In this paper, we give some recursive formulas for the number of ordered/unordered factorizations of a positive integer $n$ such that each factor is at least $\ell$. In particular, by using elementary techniques, we give an explicit formula in cases where $k=2,3,4$. | ||
| کلیدواژهها | ||
| Multiplicative partition function؛ Set partitions؛ Partition function؛ Perfect square؛ Euler's Phi function | ||
| مراجع | ||
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