Question

On $\sigma(n)=\sigma \left( \left \lfloor{e^{H_n-\gamma}}\right \rfloor \right) $, for integers $n\geq 1$

score 74 · Answer 1 · 2026-03-28 06:31:02

74

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On $\sigma(n)=\sigma \left( \left \lfloor{e^{H_n-\gamma}}\right \rfloor \right) $, for integers $n\geq 1$

Published on 28 Mar 2026 - 6:31

score 140 · Answer 2 · 2016-08-11 23:45:45

140

Views

$\frac{\lfloor x \rfloor}{x} \to 1$ as $x \to \infty$?

Published on 11 Aug 2016 - 23:45

score 5k · Answer 3 · 2016-08-14 18:34:10

5k

Views

Ceiling of logarithm of ceiling of x

Published on 14 Aug 2016 - 18:34

score 162 · Answer 4 · 2016-08-14 19:40:12

162

Views

Find the full solution to $\left\lfloor{\frac{N}{a}}\right\rfloor = \left\lfloor{\frac{N}{p}}\right\rfloor - a$ where $N \geq p^2, p > 1$

Published on 14 Aug 2016 - 19:40

score 108 · Answer 5 · 2016-08-15 14:47:23

108

Views

Equation $\left\lfloor \frac{y-y^2}{1+\frac{y2}x}\right\rfloor = a$

Published on 15 Aug 2016 - 14:47

score 1.5k · Answer 6 · 2016-08-16 16:22:57

1.5k

Views

How to prove property of greatest integer function:

Published on 16 Aug 2016 - 16:22

score 1.2k · Answer 7 · 2026-03-28 06:09:11

1.2k

Views

Pairwise sum and divide

Published on 28 Mar 2026 - 6:09

score 1.4k · Answer 8 · 2016-08-17 06:14:56

Proof about floor function: $\lfloor x\rfloor+\lfloor x + \frac{1}{n} \rfloor+\cdots + \lfloor x + \frac{(n-1)}{n} \rfloor = \lfloor nx \rfloor$

score 405 · Answer 9 · 2016-08-17 13:36:33

405

Views

Calculate $\int_{p}^{p+2} \left \lfloor{\sqrt{x}}\right \rfloor dx,$ for the sequence of the first $100$ prime pairs $(p,p+2)$

Published on 17 Aug 2016 - 13:36

score 74 · Answer 10 · 2026-03-28 06:31:02

74

Views

Smallest $n$ such that $H_{n,2^{-1}} \geq n$ where $H_{n,2^{-1}}$ are generalized Harmonic numbers

Published on 28 Mar 2026 - 6:31

score 90 · Answer 11 · 2016-08-19 19:20:56

90

Views

On simple calculations with $\sum_{k=1}^{n-1}\left\lfloor{\frac{km}{n}}\right\rfloor=\frac{1}{2}(m-1)(n-1)$ and primes $m$ and $n$

Published on 19 Aug 2016 - 19:20

score 402 · Answer 12 · 2026-03-28 06:23:25

402

Views

Simplifying $\sum_{i=1}^n{\lfloor \frac{n}{i} \rfloor}$?

Published on 28 Mar 2026 - 6:23

score 829 · Answer 13 · 2016-08-21 09:38:46

829

Views

Find all real solutions to $[x]+[2x]+[4x]+[8x]+[16x]+[32x]=12345$

Published on 21 Aug 2016 - 9:38

score 189 · Answer 14 · 2016-08-22 07:50:03

189

Views

Evaluate the following definite integral with respect to box function

Published on 22 Aug 2016 - 7:50

score 91 · Answer 15 · 2026-03-25 17:19:47

91

Views

Prove the inequality $\{\sqrt[3]{n}\}>\frac1{3\sqrt[3]{n^2}}$

Published on 25 Mar 2026 - 17:19

List Question

On $\sigma(n)=\sigma \left( \left \lfloor{e^{H_n-\gamma}}\right \rfloor \right) $, for integers $n\geq 1$

$\frac{\lfloor x \rfloor}{x} \to 1$ as $x \to \infty$?

Ceiling of logarithm of ceiling of x

Find the full solution to $\left\lfloor{\frac{N}{a}}\right\rfloor = \left\lfloor{\frac{N}{p}}\right\rfloor - a$ where $N \geq p^2, p > 1$

Equation $\left\lfloor \frac{y-y^2}{1+\frac{y2}x}\right\rfloor = a$

How to prove property of greatest integer function:

Pairwise sum and divide

Proof about floor function: $\lfloor x\rfloor+\lfloor x + \frac{1}{n} \rfloor+\cdots + \lfloor x + \frac{(n-1)}{n} \rfloor = \lfloor nx \rfloor$

Calculate $\int_{p}^{p+2} \left \lfloor{\sqrt{x}}\right \rfloor dx,$ for the sequence of the first $100$ prime pairs $(p,p+2)$

Smallest $n$ such that $H_{n,2^{-1}} \geq n$ where $H_{n,2^{-1}}$ are generalized Harmonic numbers

On simple calculations with $\sum_{k=1}^{n-1}\left\lfloor{\frac{km}{n}}\right\rfloor=\frac{1}{2}(m-1)(n-1)$ and primes $m$ and $n$

Simplifying $\sum_{i=1}^n{\lfloor \frac{n}{i} \rfloor}$?

Find all real solutions to $[x]+[2x]+[4x]+[8x]+[16x]+[32x]=12345$

Evaluate the following definite integral with respect to box function

Prove the inequality $\{\sqrt[3]{n}\}>\frac1{3\sqrt[3]{n^2}}$

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