Generalization of the property of the number of divisors function
Matematičeskoe obrazovanie, Tome 105 (2023) no. 1, pp. 2-6.

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The article studies the question under what conditions the number of representations of a natural number N as a product m of natural numbers is not divisible by m or coprime with m. The case of a simple m is studied, some generalizations to the case of a composite m are given. The work is an independent study of the author under the scientific supervision of Stern Alexandr Savelievich.
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D. E. Volovich. Generalization of the property of the number of divisors function. Matematičeskoe obrazovanie, Tome 105 (2023) no. 1, pp. 2-6. http://geodesic.mathdoc.fr/item/MO_2023_105_1_a0/