Doubly Recursive Integer Factorizations
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
The fundamental theorem of arithmetic states that every integer greater than 1 can be factored uniquely (up to the ordering of the factors) into a product of powers of one or more primes. So denoting the primes 2, 3, 5 … as , , , …, each integer can be factored as , where and are the index and power of the prime in the factorization. For example, , or .
[more]
Contributed by: Robert Dickau (September 2018)
Open content licensed under CC BY-NC-SA
Details
Snapshot 1: the integer 2 is the first prime raised to the first power, with representation
Snapshot 2: subscript and superscript are ones displayed
Snapshot 3: hiding the subscript and superscript ones changes the order of factors due to the sorting rules in Mathematica.
Reference
[1] "Riffs and Rotes." (Aug 7, 2018) oeis.org/wiki/Riffs_and_Rotes.
Snapshots
Permanent Citation