Abstract
Let \( \tilde p(n) \) be the number of partitions of a positive integer n in square free parts. We prove that for large N,
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(a)
The number of n ≤ N such that \( \tilde p(n) \) is odd is ≫ log N
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(b)
The number of n ≤ N such that \( \tilde p(n) \) is even is ≫ N/log N.
In memory of Professor Robert A. Rankin
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Zaharescu, A. (2003). On the Parity of the Number of Partitions in Square Free Parts. In: Berndt, B., Ono, K. (eds) Number Theory and Modular Forms. Developments in Mathematics, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6044-6_24
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DOI: https://doi.org/10.1007/978-1-4757-6044-6_24
Publisher Name: Springer, Boston, MA
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