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Equality of two sums involving hecke eigenvalues in a paper of Luo and Sarnak

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#number-theory #modular-forms #divisor-sum
33
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Question on an equation involving sum of a function over divisors.

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#summation #divisor-sum
124
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Finding natural numbers with $12$ divisors $1=d_1<d_2<\cdots<d_{12}=n$, such that the divisor with the index $d_4$ is equal to $1+(d_1+d_2+d_4)d_8$.

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#algebra-precalculus #elementary-number-theory #divisor-sum
75
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Prove that there are infinitely many natural number such that $σ(n)>100n$

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#elementary-number-theory #divisor-sum #multiplicative-function
67
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$\sum_{k = 1}^{\infty} k\lfloor\frac{n}{k} \rfloor = 1 + \sum_{k = 1}^n \sigma_1(n)$

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#sequences-and-series #elementary-number-theory #ceiling-and-floor-functions #divisor-sum #arithmetic-functions
152
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Extraordinary Numbers

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#prime-numbers #logarithms #divisor-sum #riemann-hypothesis
48
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Is there any square harmonic divisor number greater than $1$?

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#number-theory #reference-request #square-numbers #divisor-sum #perfect-numbers
240
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A question about prime numbers, totient function $ \phi(n) $ and sum of divisors function $ \sigma(n) $

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#number-theory #prime-numbers #totient-function #divisor-sum
119
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Prime numbers which end with $59$ or $79$

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#elementary-number-theory #prime-numbers #totient-function #divisor-sum
51
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Can the sum of odd divisors of an integer exceed n

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#divisor-sum
155
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Prime numbers which end with 03, 23, 43, 63 or 83

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#number-theory #prime-numbers #totient-function #divisor-sum
471
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Square of prime numbers

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#number-theory #prime-numbers #totient-function #divisor-sum
246
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Determine all positive integers $n$ such that: $n+d(n)+d(d(n))+\dotsb=2023$.

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#number-theory #elementary-number-theory #summation #divisor-sum
160
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Why must $n-\lfloor\frac n2\rfloor+\lfloor\frac n3\rfloor-\dotsb$ grow like $n\ln2$?

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#sequences-and-series #combinatorics #discrete-mathematics #ceiling-and-floor-functions #divisor-sum
79
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Growth rate of sum of divisors cubed

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#number-theory #elementary-number-theory #reference-request #divisor-sum

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