## On partitions and cyclotomic polynomials.(English)Zbl 1067.11510

Summary: Let $$m$$ denote a squarefree number. Let $$f_m(n)$$ denote the number of partitions of $$n$$ into parts that are relatively prime to $$m$$. Let $$\Phi_m(z)$$ denote the $$m$$th cyclotomic polynomial. We obtain a generating function for $$f_m(n)$$ that involves factors $$\Phi_m(z^n)$$.

### MSC:

 11P81 Elementary theory of partitions 05A17 Combinatorial aspects of partitions of integers 11T22 Cyclotomy
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