Question

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

score 236 · Answer 1 · 2026-05-10 17:38:57

236

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

Published on 10 May 2026 - 17:38

score 88 · Answer 2 · 2026-05-11 00:30:42

88

Views

Did Descartes and Frénicle consider deficient-perfect numbers?

Published on 11 May 2026 - 0:30

score 369 · Answer 3 · 2026-05-10 14:29:10

369

Views

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

Published on 10 May 2026 - 14:29

score 83 · Answer 4 · 2026-05-10 16:14:40

83

Views

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

Published on 10 May 2026 - 16:14

score 171 · Answer 5 · 2026-04-16 01:15:57

171

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 16 Apr 2026 - 1:15

score 48 · Answer 6 · 2026-04-16 03:56:32

48

Views

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

Published on 16 Apr 2026 - 3:56

score 62 · Answer 7 · 2026-05-11 00:32:43

62

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 11 May 2026 - 0:32

score 120 · Answer 8 · 2026-04-16 18:26:43

120

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 16 Apr 2026 - 18:26

score 105 · Answer 9 · 2026-04-15 12:04:37

105

Views

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

Published on 15 Apr 2026 - 12:04

score 345 · Answer 10 · 2026-04-16 08:24:14

345

Views

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

Published on 16 Apr 2026 - 8:24

score 637 · Answer 11 · 2026-04-10 10:44:24

637

Views

Method to find colossally abundant numbers?

Published on 10 Apr 2026 - 10:44

score 85 · Answer 12 · 2026-04-11 17:21:35

85

Views

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

Published on 11 Apr 2026 - 17:21

score 56 · Answer 13 · 2026-04-12 15:00:32

56

Views

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

Published on 12 Apr 2026 - 15:00

score 83 · Answer 14 · 2026-05-10 16:35:16

83

Views

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

Published on 10 May 2026 - 16:35

score 477 · Answer 15 · 2026-04-12 13:06:09

477

Views

Upper Bounds on a Ratio Concerning the Sum of Divisors

Published on 12 Apr 2026 - 13:06

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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