Analytic number theory | Integer sequences

Smooth number

In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is a number whose every prime factor is at most 7, so 49 = 72 and 15750 = 2 × 32 × 53 × 7 are both 7-smooth, while 11 and 702 = 2 × 33 × 13 are not 7-smooth. The term seems to have been coined by Leonard Adleman. Smooth numbers are especially important in cryptography, which relies on factorization of integers. The 2-smooth numbers are just the powers of 2, while 5-smooth numbers are known as regular numbers. (Wikipedia).

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Smooth Transition Function in One Dimension | Smooth Transition Function Part 1

#SoME2 This video gives a detailed construction of transition function for various levels of smoothness. Sketch of proofs for 4 theorems regarding smoothness: https://kaba.hilvi.org/homepage/blog/differentiable.htm Faà di Bruno's formula: https://en.wikipedia.org/wiki/Fa%C3%A0_di_Bruno%2

From playlist Summer of Math Exposition 2 videos

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A Zero-Density Approach to Smooth Numbers - Adam Harper

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From playlist Mathematics

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Linear equations in smooth numbers - Lilian Matthiesen

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From playlist Mathematics

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SmoothLife6

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From playlist SmoothLife

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In this video, I define the concept of a winding number of a curve around a point, which intuitively measures how many times a curve loops around a point. For example, for a circle (or any simple closed curve), the winding number should be 1, but for the curve in the thumbnail, the winding

From playlist Multivariable Calculus

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Dividing Complex Numbers Example

Dividing Complex Numbers Example Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys

From playlist Complex Numbers

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Ex: Determine a Number that is Less Than and Greater than Using a Specific Place Value

This video provides examples of how to find a number that is less than and greater than a given number using a specific place value. Search Video Library at http://www.mathispower4u.wordpress.com

From playlist Whole Numbers: Place Value and Writing Numbers

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Finding Critical Numbers Example 1

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding Critical Numbers Example 1. We find the critical numbers of f(x) = sin^2x + cosx on (0, 2pi).

From playlist Calculus

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From playlist CALCULUS 2 CH 11 COMPLEX NUMBERS

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From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels

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From playlist CTNT 2018 - Guest Lectures

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John Milnor: Spheres

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From playlist Abel Lectures

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Factoring with Elliptic Curves - Jeremy Teitelbaum [2018]

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From playlist Number Theory

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Elisa Lorenzo Garcia : On smooth plane models for modular curves of Shimura type

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From playlist Algebraic and Complex Geometry

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On Singularities With Rational Homology Disk Smoothings - Andras Stipsicz

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From playlist Mathematics

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Unexpected fillings, singularities, and plane curve arrangements - Laura Starkston

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From playlist Mathematics

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From playlist Probability

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2023 Number Challenge: Estimate the 2023rd Harmonic Number

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From playlist Math Problems with Number 2023

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Order (group theory) | Integer factorization | Rough number | If and only if | Lenstra elliptic-curve factorization | Størmer's theorem | Almost all | Prime-counting function | Group (mathematics) | Factor base | Cooley–Tukey FFT algorithm | Pollard's p − 1 algorithm | Power of two | Round number | Highly composite number | Regular number | Cryptography | Homomorphism | Composite number | Cryptanalysis | On-Line Encyclopedia of Integer Sequences | General number field sieve | Very smooth hash | Pohlig–Hellman algorithm | Set (mathematics) | Integer | Discrete logarithm | Number theory | Subset | Fast Fourier transform | Prime number | Dickman function | Dixon's factorization method | Quadratic sieve | Unusual number