Abstract
In this paper we introduce an arithmetical function δ(n), the difference between the number of divisors of n congruent to 1 mod 3 and those congruent to −1 mod 3. This function then is related to the classical function σ(n) which is the sum of the divisors of n. In particular we prove the identity
$$3\bigg(\sum_{n=0}^{\infty}\delta(3n+1)x^n\bigg)^2=\sum_{n=0}^{\infty}\sigma(3n+2)x^n.$$
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Farkas, H. On an Arithmetical Function. Ramanujan J 8, 309–315 (2004). https://doi.org/10.1007/s11139-004-0141-5
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DOI: https://doi.org/10.1007/s11139-004-0141-5