How to resolve the algorithm Abundant odd numbers step by step in the Maple programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Abundant odd numbers step by step in the Maple programming language
Table of Contents
Problem Statement
An Abundant number is a number n for which the sum of divisors σ(n) > 2n, or, equivalently, the sum of proper divisors (or aliquot sum) s(n) > n.
12 is abundant, it has the proper divisors 1,2,3,4 & 6 which sum to 16 ( > 12 or n); or alternately, has the sigma sum of 1,2,3,4,6 & 12 which sum to 28 ( > 24 or 2n).
Abundant numbers are common, though even abundant numbers seem to be much more common than odd abundant numbers. To make things more interesting, this task is specifically about finding odd abundant numbers.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Abundant odd numbers step by step in the Maple programming language
Source code in the maple programming language
with(NumberTheory):
# divisorSum returns the sum of the divisors of x not including x
divisorSum := proc(x::integer)
return SumOfDivisors(x) - x;
end proc:
# abundantNumber returns true if x is an abundant number and false otherwise
abundantNumber := proc(x::integer)
if (SumOfDivisors(x) > 2*x) then return true
else return false end if;
end proc:
count := 0:
number := 1:
cat("First 25 abundant odd numbers");
while count < 25 do
if (abundantNumber(number)) then
count += 1:
print(cat(count, ": ", number, " sum of divisors ", SumOfDivisors(number), " sum of proper divisors ", divisorSum(number)));
else end if;
number += 2:
end:
while (count < 1000) do
if (abundantNumber(number)) then
count += 1:
else end if:
number += 2:
end:
cat("The 1000th odd abundant number is ", number - 2, ", its sum of divisors is ", SumOfDivisors(number - 2), ", and its sum of proper divisors is ", divisorSum(number - 2));
for number from 10^9 + 1 by 2 to infinity while not abundantNumber(number) do end:
cat("First abundant odd number > 10^9 is ", number, ", its sum of divisors is ", SumOfDivisors(number), ", and its sum of proper divisors is ",divisorSum(number));
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