Question

The number of divisors of a number whose sum of divisors is a perfect square

score 1.9k · Answer 1 · 2015-01-26 16:16:45

1.9k

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The number of divisors of a number whose sum of divisors is a perfect square

Published on 26 Jan 2015 - 16:16

score 3.3k · Answer 2 · 2015-01-26 22:13:27

3.3k

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Can someone help me prove that $\tau(n)$ is odd iff $n$ is a perfect square.

Published on 26 Jan 2015 - 22:13

score 28.9k · Answer 3 · 2015-01-30 02:42:25

28.9k

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Product of Divisors of some $n$ proof

Published on 30 Jan 2015 - 2:42

score 399 · Answer 4 · 2026-03-25 09:31:32

399

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$d(n)$ is odd iff $n = k^2$

Published on 25 Mar 2026 - 9:31

score 68 · Answer 5 · 2015-02-01 16:36:04

68

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Find an $n$ not a power of a prime such that $n$ has 51 positive divisors

Published on 01 Feb 2015 - 16:36

score 62 · Answer 6 · 2015-02-20 15:22:38

62

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proofs of $n\sum_{d|n}\frac{(-1)^{d+1}}{d}=\sum_{d|n,d \text{ odd}}d$

Published on 20 Feb 2015 - 15:22

score 131 · Answer 7 · 2015-03-05 06:36:42

131

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Analogue to superior highly composite numbers for the unitary divisor function

Published on 05 Mar 2015 - 6:36

score 667 · Answer 8 · 2015-04-16 02:01:03

667

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Can two integers have the same product of divisors?

Published on 16 Apr 2015 - 2:01

score 99 · Answer 9 · 2015-04-23 15:15:55

99

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Number of Divisors of most numbers

Published on 23 Apr 2015 - 15:15

score 951 · Answer 10 · 2026-03-25 19:51:39

951

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Euler's totient and divisors count function relationship when $[(\frac{\varphi(n)}{2}+1)\cdot(\frac{\tau(n)}{2}+1)] = n$

Published on 25 Mar 2026 - 19:51

score 663 · Answer 11 · 2015-05-06 11:28:47

663

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Numbers having in decimal representation no common digits with all their proper divisors

Published on 06 May 2015 - 11:28

score 175 · Answer 12 · 2015-06-02 15:02:48

175

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Show $\forall\varepsilon>0\,\lim_{n\to\infty}\frac{\#\{\text{positive divisors of n}\}}{n^\varepsilon}=0$

Published on 02 Jun 2015 - 15:02

score 38 · Answer 13 · 2015-07-05 18:09:13

38

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Number Theoretic Sum of three variables. Having trouble isolating two of them.

Published on 05 Jul 2015 - 18:09

score 531 · Answer 14 · 2015-07-08 02:20:40

531

Views

Probability a string has $2$ digits, $4$ consonants, and $1$ vowel, given a length of $7$ w/o repetition

Published on 08 Jul 2015 - 2:20

score 2.5k · Answer 15 · 2026-03-25 19:51:33

2.5k

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Number theory proof for why $\tau$, the number of divisors of $n$ is multiplicative

Published on 25 Mar 2026 - 19:51

List Question

The number of divisors of a number whose sum of divisors is a perfect square

Can someone help me prove that $\tau(n)$ is odd iff $n$ is a perfect square.

Product of Divisors of some $n$ proof

$d(n)$ is odd iff $n = k^2$

Find an $n$ not a power of a prime such that $n$ has 51 positive divisors

proofs of $n\sum_{d|n}\frac{(-1)^{d+1}}{d}=\sum_{d|n,d \text{ odd}}d$

Analogue to superior highly composite numbers for the unitary divisor function

Can two integers have the same product of divisors?

Number of Divisors of most numbers

Euler's totient and divisors count function relationship when $[(\frac{\varphi(n)}{2}+1)\cdot(\frac{\tau(n)}{2}+1)] = n$

Numbers having in decimal representation no common digits with all their proper divisors

Show $\forall\varepsilon>0\,\lim_{n\to\infty}\frac{\#\{\text{positive divisors of n}\}}{n^\varepsilon}=0$

Number Theoretic Sum of three variables. Having trouble isolating two of them.

Probability a string has $2$ digits, $4$ consonants, and $1$ vowel, given a length of $7$ w/o repetition

Number theory proof for why $\tau$, the number of divisors of $n$ is multiplicative

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