A034683: Unitary abundant numbers: numbers k such that usigma(k) > 2*k
A034683 ➡️ https://oeis.org/A034683

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/Unitary_abundant_numbers.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/Unitary_abundant_numbers.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/Unitary_abundant_numbers.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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A034048: Numbers with multiplicative digital root value 0
A034048 ➡️ https://oeis.org/A034048

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A034048.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A034048.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A034048.html

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A034020: Not of the form x^2 + x*y + y^2
A034020 ➡️ https://oeis.org/A034020

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A034020.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A034020.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A034020.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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A034017: Numbers that are primitively represented by x^2 + xy + y^2
A034017 ➡️ https://oeis.org/A034017

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A034017.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A034017.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A034017.html

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A033950: Refactorable numbers: number of divisors of k divides k. Also known as tau numbers
A033950 ➡️ https://oeis.org/A033950

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

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

#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

A033949: Positive integers that do not have a primitive root
A033949 ➡️ https://oeis.org/A033949

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A033949.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A033949.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A033949.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

A033948: Numbers that have a primitive root (k such that the multiplicative group modulo k is cyclic)
A033948 ➡️ https://oeis.org/A033948

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A033948.html
3D graph Gen, threejs animation ➡️ https://decompwlj.com/3DgraphGen/A033948.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A033948.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