Question

How many divisors can $bx$ have, given the number of divisors of $b$ and $x$?

score 97 · Answer 1 · 2013-06-18 12:23:48

97

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How many divisors can $bx$ have, given the number of divisors of $b$ and $x$?

Published on 18 Jun 2013 - 12:23

score 158 · Answer 2 · 2013-08-06 09:17:36

158

Views

Prove that if $\sigma(F_a)<\sigma(F_b)$, where $1 \leq b < a$, then $\sigma(a)<\sigma(b)$ also

Published on 06 Aug 2013 - 9:17

score 198 · Answer 3 · 2026-03-30 02:07:51

198

Views

Prove that $|n-\frac{\sigma_0(n)\phi(n)}{2}|$ equal to a prime implies that n is a semiprime

Published on 30 Mar 2026 - 2:07

score 229 · Answer 4 · 2013-08-09 13:20:47

229

Views

Prove that $\sum_{n=1}^\infty \frac{\sigma_a(n)}{n^s}=\zeta(s)\zeta(s-a)$

Published on 09 Aug 2013 - 13:20

score 602 · Answer 5 · 2013-08-13 06:05:23

602

Views

Prove that if $F_n$ is highly abundant, then so is $n$.

Published on 13 Aug 2013 - 6:05

score 1.4k · Answer 6 · 2013-08-18 18:19:39

1.4k

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Find two-digit numbers such that their ratio equals $0.254902$.

Published on 18 Aug 2013 - 18:19

score 203 · Answer 7 · 2013-08-25 13:30:12

203

Views

Prove that all practical numbers not of the form $2^n$ are pseudoperfect

Published on 25 Aug 2013 - 13:30

score 731 · Answer 8 · 2013-08-27 06:14:03

Prove that every highly abundant or highly composite number $k$ is a prime distance from the nearest primes $\ne k \pm 1$ on either side

score 541 · Answer 9 · 2013-09-08 08:54:57

541

Views

Divisor Function

Published on 08 Sep 2013 - 8:54

score 80 · Answer 10 · 2013-09-13 11:00:29

80

Views

Prove that $n \equiv \pm 1 \bmod 6 \implies \sigma(n)<2n$ i.e. $n$ is deficient.

Published on 13 Sep 2013 - 11:00

score 256 · Answer 11 · 2013-09-24 05:19:16

256

Views

Prove that every harmonic divisor number is semiperfect (eq there are no weird harmonic divisor numbers)

Published on 24 Sep 2013 - 5:19

score 352 · Answer 12 · 2026-03-27 01:46:12

352

Views

Are all known $k$-multiperfect numbers (for $k > 2$) not squarefree?

Published on 27 Mar 2026 - 1:46

score 486 · Answer 13 · 2013-10-05 03:45:54

486

Views

Does the sum of reciprocals of the harmonic divisor numbers converge?

Published on 05 Oct 2013 - 3:45

score 140 · Answer 14 · 2013-10-05 11:55:19

140

Views

To prove $6|σ(6n-1) , ∀n∈ \mathbb N$

Published on 05 Oct 2013 - 11:55

score 51 · Answer 15 · 2013-10-19 12:27:38

51

Views

greater divior polynomials

Published on 19 Oct 2013 - 12:27

List Question

How many divisors can $bx$ have, given the number of divisors of $b$ and $x$?

Prove that if $\sigma(F_a)<\sigma(F_b)$, where $1 \leq b < a$, then $\sigma(a)<\sigma(b)$ also

Prove that $|n-\frac{\sigma_0(n)\phi(n)}{2}|$ equal to a prime implies that n is a semiprime

Prove that $\sum_{n=1}^\infty \frac{\sigma_a(n)}{n^s}=\zeta(s)\zeta(s-a)$

Prove that if $F_n$ is highly abundant, then so is $n$.

Find two-digit numbers such that their ratio equals $0.254902$.

Prove that all practical numbers not of the form $2^n$ are pseudoperfect

Prove that every highly abundant or highly composite number $k$ is a prime distance from the nearest primes $\ne k \pm 1$ on either side

Divisor Function

Prove that $n \equiv \pm 1 \bmod 6 \implies \sigma(n)<2n$ i.e. $n$ is deficient.

Prove that every harmonic divisor number is semiperfect (eq there are no weird harmonic divisor numbers)

Are all known $k$-multiperfect numbers (for $k > 2$) not squarefree?

Does the sum of reciprocals of the harmonic divisor numbers converge?

To prove $6|σ(6n-1) , ∀n∈ \mathbb N$

greater divior polynomials

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