Question

Can this relationship between the Harmonic Number, Mertens, and Sum-of-Divisors functions be proven?

score 232 · Answer 1 · 2019-06-23 21:18:26

232

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Can this relationship between the Harmonic Number, Mertens, and Sum-of-Divisors functions be proven?

Published on 23 Jun 2019 - 21:18

score 84 · Answer 2 · 2019-06-24 19:57:08

84

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Did Descartes and Frénicle consider deficient-perfect numbers?

Published on 24 Jun 2019 - 19:57

score 357 · Answer 3 · 2026-03-25 01:21:55

357

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Question on Divisor Sum over the Liouville Function $\lambda(d)=(-1)^{\omega(d)}$

Published on 25 Mar 2026 - 1:21

score 80 · Answer 4 · 2026-03-25 06:06:38

80

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How often is $N/(2N-\sigma(N))$ a palindrome (in base-$10$) if $N$ is deficient-perfect?

Published on 25 Mar 2026 - 6:06

score 168 · Answer 5 · 2019-07-01 19:03:49

168

Views

Any suggestions on a closed form of $\sum_{a=1}^{N} \left({\lfloor{\frac{N+1}{a}}\rfloor+\lfloor{\frac{N-1}{a}}\rfloor}\right)$

Published on 01 Jul 2019 - 19:03

score 45 · Answer 6 · 2019-07-05 18:48:37

45

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When is $\sigma(q^{k-1})$ a square when $q \equiv 1 \pmod 4$ and $k \equiv 1 \pmod 4$?

Published on 05 Jul 2019 - 18:48

score 58 · Answer 7 · 2019-07-05 20:24:28

58

Views

Is there a specific equation relating $\varphi(N)$ to $\sigma(N)$ when $N = q^k n^2$ is an odd perfect number?

Published on 05 Jul 2019 - 20:24

score 117 · Answer 8 · 2019-07-06 06:06:54

117

Views

If $q$ is prime, can $\sigma(q^{k-1})$ and $\sigma(q^k)/2$ be both squares when $q \equiv 1 \pmod 4$ and $k \equiv 1 \pmod 4$?

Published on 06 Jul 2019 - 6:06

score 103 · Answer 9 · 2019-07-07 19:10:08

103

Views

Miscellaneous conjectures about perfect numbers related to the quantity $\varphi\left(103\frac{\sigma(n)}{2}+107n\right)$

Published on 07 Jul 2019 - 19:10

score 342 · Answer 10 · 2019-07-09 10:13:30

342

Views

Fast Computation of the Divisor Summatory Function $\sum_{i=1}^x\sum_{d|i}d$

Published on 09 Jul 2019 - 10:13

score 634 · Answer 11 · 2019-07-10 05:47:13

634

Views

Method to find colossally abundant numbers?

Published on 10 Jul 2019 - 5:47

score 82 · Answer 12 · 2019-07-10 13:09:03

82

Views

Tight Bounds on the Sum and Difference of Divisors of RSA Challenge Numbers

Published on 10 Jul 2019 - 13:09

score 53 · Answer 13 · 2019-07-12 04:52:09

53

Views

Determine whether the $2$-densely divisible numbers are the same as the $k$-practical numbers as $k$ goes to infinity.

Published on 12 Jul 2019 - 4:52

score 82 · Answer 14 · 2026-03-25 11:07:01

82

Views

Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

Published on 25 Mar 2026 - 11:07

score 474 · Answer 15 · 2019-07-22 00:30:29

474

Views

Upper Bounds on a Ratio Concerning the Sum of Divisors

Published on 22 Jul 2019 - 0:30

List Question

Can this relationship between the Harmonic Number, Mertens, and Sum-of-Divisors functions be proven?

Did Descartes and Frénicle consider deficient-perfect numbers?

Question on Divisor Sum over the Liouville Function $\lambda(d)=(-1)^{\omega(d)}$

How often is $N/(2N-\sigma(N))$ a palindrome (in base-$10$) if $N$ is deficient-perfect?

Any suggestions on a closed form of $\sum_{a=1}^{N} \left({\lfloor{\frac{N+1}{a}}\rfloor+\lfloor{\frac{N-1}{a}}\rfloor}\right)$

When is $\sigma(q^{k-1})$ a square when $q \equiv 1 \pmod 4$ and $k \equiv 1 \pmod 4$?

Is there a specific equation relating $\varphi(N)$ to $\sigma(N)$ when $N = q^k n^2$ is an odd perfect number?

If $q$ is prime, can $\sigma(q^{k-1})$ and $\sigma(q^k)/2$ be both squares when $q \equiv 1 \pmod 4$ and $k \equiv 1 \pmod 4$?

Miscellaneous conjectures about perfect numbers related to the quantity $\varphi\left(103\frac{\sigma(n)}{2}+107n\right)$

Fast Computation of the Divisor Summatory Function $\sum_{i=1}^x\sum_{d|i}d$

Method to find colossally abundant numbers?

Tight Bounds on the Sum and Difference of Divisors of RSA Challenge Numbers

Determine whether the $2$-densely divisible numbers are the same as the $k$-practical numbers as $k$ goes to infinity.

Are there (restricted) instances when the deficiency and sum-of-proper-divisors functions are multiplicative?

Upper Bounds on a Ratio Concerning the Sum of Divisors

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