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Idempotent help

Hello my fellow Sage users. I'm trying to come up ith a formula in sage that relates the number of idempotents in Zn with the number of distinct prime factors that n has. Talking about idempotent rings in my class has gotten a few students confused and this formula will help me better explain the concept. Thank you. Any pointers in the right direction would help greatly.

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Idempotent help

Hello my fellow Sage users. I'm trying to come up ith a formula in sage that relates the number of idempotents in Zn with the number of distinct prime factors that n has. Talking about idempotent rings in my class has gotten a few students confused and this formula will help me better explain the concept. Thank you. Any pointers in the right direction would help greatly.