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Answer by Fedor Petrov for Generating function for numbers divisible by some...
This is probably not what you look for, but you may denote $N=\prod p_i$, $m_i=N/p_i$, then consider a polynomial $$q(x)=\prod_i (x^{m_i}+x^{2m_i}+\dots+x^{(p_i-1)m_i}).$$Your generating function...
View ArticleGenerating function for numbers divisible by some primes
Consider the first $k$ primes $p_1 = 2, p_2 = 3, \dots, p_k$. Let $A_k$ be the set of numbers that are divisible by at least one $p_i$. We can represent this set as a generating function:$$G_k(x) =...
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