List questions from divisor-counting-function

Published on 21 Mar 2026 - 22:06

128

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$\tau (x) = 2016$ and for least $x = a \times b^2$ find $b$.

Published on 22 Mar 2026 - 0:24

422

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Interesting resolution to considering prime factorisations and finding the number of positive divisors of large numbers??

Published on 21 Mar 2026 - 21:23

2k

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Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

Published on 25 Mar 2026 - 14:46

63

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Is there a function $s(n)$ which tells the amount of factors any $n$ has?

Published on 21 Mar 2026 - 22:51

75

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Is there an equation that relates the parity of $\sigma_0$ to the parity of $\sigma_1$?

Published on 21 Mar 2026 - 20:23

599

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Identity for the divisor function: $\tau(mn)=\sum\limits_{d\mid(m,n)}\mu(d) \tau(m/d)\tau(n/d)$

Published on 22 Mar 2026 - 12:10

306

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Why so many numbers with 12 divisors?

Published on 22 Mar 2026 - 7:28

107

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explicit exact formula for divisor functions and sums

Published on 22 Mar 2026 - 11:09

129

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Fundamental principles of counting

Published on 25 Mar 2026 - 10:53

2.2k

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How many ways are there to put five identical red balls and eight identical blue balls into 20 distinct boxes.

Published on 22 Mar 2026 - 5:22

64

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Determine the number of strings of length five consisting of five distinct capital letters (A-Z)

Published on 22 Mar 2026 - 6:42

708

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Can you give me a big number with many divisors?

Published on 22 Mar 2026 - 7:40

36

Views

pigeonhole principle

Published on 23 Mar 2026 - 15:09

87

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counting number of square unit the line should travel

Published on 21 Mar 2026 - 23:46

List Question

Stuck at evaluating $\sum\limits_{d \mid n} \tau(d)$

$\tau (x) = 2016$ and for least $x = a \times b^2$ find $b$.

Interesting resolution to considering prime factorisations and finding the number of positive divisors of large numbers??

Showing $\sum_{d\mid n} \mu(d)\tau(n/d)=1$ and $\sum_{d\mid n} \mu(d)\tau(d)=(-1)^r$

Is there a function $s(n)$ which tells the amount of factors any $n$ has?

Is there an equation that relates the parity of $\sigma_0$ to the parity of $\sigma_1$?

Identity for the divisor function: $\tau(mn)=\sum\limits_{d\mid(m,n)}\mu(d) \tau(m/d)\tau(n/d)$

Why so many numbers with 12 divisors?

explicit exact formula for divisor functions and sums

Fundamental principles of counting

How many ways are there to put five identical red balls and eight identical blue balls into 20 distinct boxes.

Determine the number of strings of length five consisting of five distinct capital letters (A-Z)

Can you give me a big number with many divisors?

pigeonhole principle

counting number of square unit the line should travel

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