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(max_bound) * sum(forall a <= max_bound)( (a^(k-1) * e^(-a/s(a)) / k! * s(a)^k) ) More...

#include <assert.h>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>

Include dependency graph for huer_model.c:

Macros
#define	UPPERPARENTS 16

Functions
uint64_t	s (uint64_t n)

uint64_t	factorial (uint64_t n)

double	accumulator (uint64_t start_a, char k, uint64_t propSumDiv, long double acc)

int	main (int argc, char *argv[])

Variables
int	numChunks = 10

int	chunk_size

int	buffer_size

Detailed Description

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(max_bound) * sum(forall a <= max_bound)( (a^(k-1) * e^(-a/s(a)) / k! * s(a)^k) )

Author: Gavin Guinn (gavin.nosp@m.guin.nosp@m.n1@gm.nosp@m.ail..nosp@m.com)

Date: 2022-02-24

Macros

Functions

Variables

Detailed Description