Aliquot Sequence Research
2.0
Compute properties of the sum-of-proper-divisors function.
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▼ factor | |
factor.h | |
primes.h | |
▼ pollpom_kparent | |
pollpom_kparent.c | This program implements an generaliztion of Conj. 1.4 of Pollack/Pomerance "Some problems of Erdos on the Sum of Divisors Function" Instead of estimating the natural density of only aliqout orphans this program also estimates the density of k-parent aliquot numbers n is a k-parent aliqout number iff there are k distinct natural numbers m st s(m) = n An aliquot orphan is a 0-parent aliquot number let delta-k be the estimated density of k-parent aliquot numbers and s(n) be the sum-of-proper-divisors function delta-k = 1/log(bound) * sum(forall a <= bound)( (a^(k-1) * e^(-a/s(a)) / k! * s(a)^k) ) |
pollpom_kparent.h | |
pollpom_kparent_cli.c | |
▼ pomyang_kparent | |
▼ inc | |
bruteforce_kparent.h | Api to brute force number of preimages |
math_macros.h | |
moewsmoews_sieve.h | Api to the Moews and Moews sieving algorithm |
PackedArray.h | |
pomyang_kparent.h | Api for pom_yang algorithm operations |
▼ src | |
bruteforce_kparent.c | Uses a simple bruteforce method to compute number of preimages for even number upto bound. Useful as a backstop test to the pom_yang algorithm |
geomean_sn.c | Runs geomean calculation from [Chum et al.] Sect 2 |
moewsmoews_sieve.c | Functions to sieve blocks of sigma function |
pomyang_cli_main.c | Command line interface to interact with the pom_yang algorithm |
pomyang_kparent.c | Counts the even numbers with k-preimages under the sum-of-proper-divisors function |