pollpom_kparent.c File Reference

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) ) More...

#include "../pollpom_kparent/pollpom_kparent.h"
#include <alloca.h>
#include <assert.h>
#include <math.h>
#include <omp.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <unistd.h>
#include "../factor/factor.h"
#include "../pomyang_kparent/inc/math_macros.h"

Include dependency graph for pollpom_kparent.c:

Functions
void	pollpom_kparent (pollpom_config_t *cfg)

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(bound) * sum(forall a <= 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

Copyright

Copyright (c) 2022

Function Documentation

pollpom_kparent()

void pollpom_kparent

(

pollpom_config_t *

cfg

)

Parameters

cfg