Lmst

#totient

One day, one decomposition
A002180: Values taken by the half-totient function phi(m)/2

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A002180.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A002180.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A002180.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #half #totient #function #phi #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A002180 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A002180 in 2D (log(weight), log(level))

One day, one decomposition
A002174: Values taken by reduced totient function psi(n)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A002174.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A002174.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A002174.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #reduced #totient #function #psi #numbers #primes #PrimeNumbers #palindromes #animation #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #sieve #fundamental #theorem #arithmetic #research

Decomposition into weight × level + jump of A002174 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A002174 in 2D (log(weight), log(level))

One day, one decomposition
A001838: Numbers k such that phi(k+2) = phi(k) + 2

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A001838.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A001838.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A001838.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #phi #Euler #totient #function #graph #threejs #webGL

Decomposition into weight × level + jump of A001838 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A001838 in 2D (log(weight), log(level))

One day, one decomposition
A001494: Numbers k such that phi(k) = phi(k+2)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A001494.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A001494.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A001494.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #Euler #totient #function #phi #graph #threejs #webGL

Decomposition into weight × level + jump of A001494 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Decomposition into weight × level + jump of A001494 in 2D (log(weight), log(level))

One day, one decomposition
A217139: Numbers n such that phi(n) = phi(n+12), with Euler's totient function phi = A000010

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A217139.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A217139.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #Euler #totient #function #phi #graph #threejs #webGL

Decomposition into weight × level + jump of A217139 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A217139 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

One day, one decomposition
A179188: Numbers n such that phi(n) = phi(n+6), with Euler's totient function phi=A000010

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A179188.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A179188.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #Euler #totient #function #graph #threejs #webGL

Decomposition into weight × level + jump of A179188 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A179188 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

One day, one decomposition
A179186: Numbers n such that phi(n) = phi(n+4), with Euler's totient function phi=A000010

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A179186.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A179186.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #Euler #totient #function #graph #threejs #webGL

Decomposition into weight × level + jump of A179186 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A179186 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

Trying to illustrate why ϕ(𝑎𝑏)=ϕ(𝑎)ϕ(𝑏) but I don't think this quite gets there.

On the left we have the 24 numbers that are coprime with 70, highlighted in a 7*10 grid. On the right these numbers appear in 6 columns of 4 each, because phi(7) = 6 and phi(10) = 4, using the mapping z -> (z mod 7, z mod 10).

One day, one decomposition
A054741: Numbers m such that totient(m) < cototient(m)

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A054741.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A054741.html

#decompwlj #maths #mathematics #sequence #OEIS #javascript #php #3D #numbers #totient #cototient #graph #threejs #webGL

Decomposition into weight × level + jump of A054741 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A054741 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

One day, one decomposition
A002202: Values taken by totient function phi(m)

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A002202.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A002202.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #integer #number #totient #function #graph

Decomposition into weight × level + jump of A002202 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A002202 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

One day, one decomposition
A002174: Values taken by reduced totient function psi(n)

3D graph #threejs #webGL ➡️ https://decompwlj.com/3Dgraph/A002174.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A002174.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #integer #number #reduced #totient #function #graph

Decomposition into weight × level + jump of A002174 in 2D (log(weight), log(level))

Decomposition into weight × level + jump of A002145 in 3D (threejs - WebGL) (log(weight), log(level), log(jump))

https://www.youtube.com/watch?v=EK32jo7i5LQ

#dirichlet #euler #primes #totient #patterns #spirals #mod #residue #class #polar #math #amazing #plot #3blue1brown

Client Info

Server: https://mastodon.social

Version: 2025.07

Repository: https://github.com/cyevgeniy/lmst