A005277: Nontotients: even numbers k such that phi(m) = k has no solution.
A005277 ➡️ https://oeis.org/A005277

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

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We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.

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A005244: A self-generating sequence: start with 2 and 3, take all products of any 2 previous elements, subtract 1 and adjoin them to the sequence
A005244 ➡️ https://oeis.org/A005244

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005244.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005244.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005244.html

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A005236: Barriers for omega(n): numbers n such that, for all m < n, m + omega(m) <= n
A005236 ➡️ https://oeis.org/A005236

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005236.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005236.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005236.html

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My first, favorite and most important sequence, the weights of prime numbers: A117078
We see prime numbers classified by level and by weight on the graph.

A117078: a(n) is the smallest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists ➡️ https://oeis.org/A117078

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A005228: Sequence and first differences (A030124) together list all positive numbers exactly once
A005228 ➡️ https://oeis.org/A005228

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005228.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005228.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005228.html

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A005214: Triangular numbers together with squares (excluding 0)
A005214 ➡️ https://oeis.org/A005214

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A005214.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A005214.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A005214.html

#decompwlj #math #mathematics #maths #sequence #OEIS #JavaScript #php #graph #3D #threejs #webGL #triangular #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 prime numbers:
- a new classification of primes ➡️ https://decompwlj.com/primedecomp.php
- in 3D - threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Prime_numbers.html

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A005153: Practical numbers: positive integers m such that every k <= sigma(m) is a sum of distinct divisors of m. Also called panarithmic numbers
A005153 ➡️ https://oeis.org/A005153

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

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

A005117: Squarefree numbers: numbers that are not divisible by a square greater than 1
A005117 ➡️ https://oeis.org/A005117

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

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