Question

Slight variation of Mertens' third theorem. Do we have an estimate of $\sum_{d \mid n\#}(-1)^{\omega(d)}\dfrac{\sigma_0(d)}{d}$?

score 157 · Answer 1 · 2026-04-16 15:43:56

157

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Slight variation of Mertens' third theorem. Do we have an estimate of $\sum_{d \mid n\#}(-1)^{\omega(d)}\dfrac{\sigma_0(d)}{d}$?

Published on 16 Apr 2026 - 15:43

score 61 · Answer 2 · 2026-04-10 04:21:15

61

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Titchmarsh divisor problem

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score 145 · Answer 3 · 2026-04-14 03:42:05

145

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Every integer is the sum of a prime and a square-free

Published on 14 Apr 2026 - 3:42

score 52 · Answer 4 · 2026-04-12 05:12:22

52

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Do we have the following property about positive integer sequences?

Published on 12 Apr 2026 - 5:12

score 199 · Answer 5 · 2026-04-16 18:52:54

199

Views

Prove that $\sum_{d|n}\mu(d)\log^m d=0$

Published on 16 Apr 2026 - 18:52

score 496 · Answer 6 · 2026-04-17 01:16:44

496

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Product form of Mobius Inversion formula: $g(n)=\prod_{d|n}f(d)^{a(n/d)}\iff f(n)=\prod_{d|n} g(d)^{b(n/d)}$

Published on 17 Apr 2026 - 1:16

score 162 · Answer 7 · 2026-04-17 09:12:51

162

Views

$\varphi(x,n)=\sum_{d|n}\mu(d)\left\lfloor\frac xd\right\rfloor$ and $\sum_{d|n}\varphi\left(\frac xd,\frac nd\right)=\lfloor x\rfloor$

Published on 17 Apr 2026 - 9:12

score 90 · Answer 8 · 2026-04-15 03:34:06

90

Views

Difference between the usage of Big-Omega notation as used by Computer Scientists and Mathematicians.

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score 101 · Answer 9 · 2026-04-14 16:58:18

101

Views

Show that $\sum_{n\le x}\max(n)=O(x)$

Published on 14 Apr 2026 - 16:58

score 65 · Answer 10 · 2026-04-19 16:31:27

65

Views

Can I define topology on Schwartz-Bruhat function space without using direct limit？

Published on 19 Apr 2026 - 16:31

score 58 · Answer 11 · 2026-04-14 23:41:07

58

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Trigonometric sum over primes estimating

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score 69 · Answer 12 · 2026-04-15 23:54:22

69

Views

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score 106 · Answer 13 · 2026-04-14 16:57:18

106

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score 46 · Answer 14 · 2026-04-13 22:46:17

46

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Why are the fowlloing sequences important ? (Bailey)

Published on 13 Apr 2026 - 22:46

score 114 · Answer 15 · 2026-04-13 22:10:23

114

Views

On asymptotic of logarithm of modulus of a function

Published on 13 Apr 2026 - 22:10

List Question

Slight variation of Mertens' third theorem. Do we have an estimate of $\sum_{d \mid n\#}(-1)^{\omega(d)}\dfrac{\sigma_0(d)}{d}$?

Titchmarsh divisor problem

Every integer is the sum of a prime and a square-free

Do we have the following property about positive integer sequences?

Prove that $\sum_{d|n}\mu(d)\log^m d=0$

Product form of Mobius Inversion formula: $g(n)=\prod_{d|n}f(d)^{a(n/d)}\iff f(n)=\prod_{d|n} g(d)^{b(n/d)}$

$\varphi(x,n)=\sum_{d|n}\mu(d)\left\lfloor\frac xd\right\rfloor$ and $\sum_{d|n}\varphi\left(\frac xd,\frac nd\right)=\lfloor x\rfloor$

Difference between the usage of Big-Omega notation as used by Computer Scientists and Mathematicians.

Show that $\sum_{n\le x}\max(n)=O(x)$

Can I define topology on Schwartz-Bruhat function space without using direct limit？

Trigonometric sum over primes estimating

Littlewood's theorem on sign changes of $\text{li}-\pi(x)$

On an integral over $\log\zeta(s)$

Why are the fowlloing sequences important ? (Bailey)

On asymptotic of logarithm of modulus of a function

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