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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2023 Volume 220, Pages 61–70 (Mi into1118)

On infinite products of Euler type

E. V. Lukyanova, M. P. Burlakov

Moscow State Pedagogical University

Abstract: In this paper, we consider recurrent and general formulas expressing the number of representations of a natural number $n$ by sums of other natural numbers in terms of sums of divisors of a given natural number.

Keywords: infinite product, additive partition of numbers, recurrent formula, arithmetic function.

UDC: 517.28, 519.101

MSC: 05A15, 11A25, 26A99

DOI: 10.36535/0233-6723-2023-220-61-70



© Steklov Math. Inst. of RAS, 2025