Question

Convergence of $\sum_{k=1}^\infty\frac{\operatorname{rad}(k!)}{\operatorname{lcm}(1,2,\ldots,k)}$

score 190 · Answer 1 · 2026-03-21 21:00:14

190

Views

Convergence of $\sum_{k=1}^\infty\frac{\operatorname{rad}(k!)}{\operatorname{lcm}(1,2,\ldots,k)}$

Published on 21 Mar 2026 - 21:00

score 162 · Answer 2 · 2018-05-31 23:08:19

162

Views

Natural density of integers such that $\forall 1\leq k\leq n-1$ satisfy $\operatorname{rad}(k)+\operatorname{rad}(n-k)\geq \operatorname{rad}(n)$

Published on 31 May 2018 - 23:08

score 161 · Answer 3 · 2026-03-25 04:43:32

161

Views

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

Published on 25 Mar 2026 - 4:43

score 113 · Answer 4 · 2026-03-17 11:01:24

113

Views

Finish the exercise to find or count the solutions of the equation $n x^2-\operatorname{rad}(n)=y^3$ over positive integers

Published on 17 Mar 2026 - 11:01

score 242 · Answer 5 · 2018-06-04 13:48:33

242

Views

Square-free integers in the sequence $n^{\operatorname{rad}(n)}+\operatorname{rad}(n)+1$

Published on 04 Jun 2018 - 13:48

score 78 · Answer 6 · 2026-03-25 04:42:37

78

Views

On the equation $\sigma(m)=105k$ over odd integers $m\geq 1$, and the deficiency of its solutions

Published on 25 Mar 2026 - 4:42

score 151 · Answer 7 · 2026-03-25 04:42:50

151

Views

Estimation of the number of solutions for the equation $\sigma(\varphi(n))=\sigma(\operatorname{rad}(n))$

Published on 25 Mar 2026 - 4:42

score 217 · Answer 8 · 2026-03-25 03:03:53

217

Views

On $\text{Lower bound}\leq \operatorname{rad}(n)$, where $n$ is an odd perfect number: reference request or what work can be done about it

Published on 25 Mar 2026 - 3:03

score 121 · Answer 9 · 2018-06-08 16:20:21

121

Views

Does this function similar to an "inverse primorial" already have a well-known label?

Published on 08 Jun 2018 - 16:20

score 116 · Answer 10 · 2026-03-25 04:41:32

116

Views

Is there a lower bound for $\operatorname{rad}(n)$ in terms of $n \in \mathbb{N}$?

Published on 25 Mar 2026 - 4:41

score 44 · Answer 11 · 2026-03-25 01:18:48

44

Views

Proof check and Are these conditions sufficient for p prime to imply p irreducible?

Published on 25 Mar 2026 - 1:18

score 80 · Answer 12 · 2018-06-10 18:41:21

80

Views

Inequalities for $\operatorname{rad}(n\text{th pentagonal number})$ and the diagonal of the regular pentagon that represents this polygonal number

Published on 10 Jun 2018 - 18:41

score 45 · Answer 13 · 2018-06-12 06:44:18

45

Views

Rules for factors of a composite number

Published on 12 Jun 2018 - 6:44

score 751 · Answer 14 · 2018-06-13 16:47:01

751

Views

Find the prime factors of $3^{32}-2^{32}$

Published on 13 Jun 2018 - 16:47

score 93 · Answer 15 · 2018-06-13 17:04:43

93

Views

Working with divisor function

Published on 13 Jun 2018 - 17:04

List Question

Convergence of $\sum_{k=1}^\infty\frac{\operatorname{rad}(k!)}{\operatorname{lcm}(1,2,\ldots,k)}$

Natural density of integers such that $\forall 1\leq k\leq n-1$ satisfy $\operatorname{rad}(k)+\operatorname{rad}(n-k)\geq \operatorname{rad}(n)$

On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$

Finish the exercise to find or count the solutions of the equation $n x^2-\operatorname{rad}(n)=y^3$ over positive integers

Square-free integers in the sequence $n^{\operatorname{rad}(n)}+\operatorname{rad}(n)+1$

On the equation $\sigma(m)=105k$ over odd integers $m\geq 1$, and the deficiency of its solutions

Estimation of the number of solutions for the equation $\sigma(\varphi(n))=\sigma(\operatorname{rad}(n))$

On $\text{Lower bound}\leq \operatorname{rad}(n)$, where $n$ is an odd perfect number: reference request or what work can be done about it

Does this function similar to an "inverse primorial" already have a well-known label?

Is there a lower bound for $\operatorname{rad}(n)$ in terms of $n \in \mathbb{N}$?

Proof check and Are these conditions sufficient for p prime to imply p irreducible?

Inequalities for $\operatorname{rad}(n\text{th pentagonal number})$ and the diagonal of the regular pentagon that represents this polygonal number

Rules for factors of a composite number

Find the prime factors of $3^{32}-2^{32}$

Working with divisor function

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