How to resolve the algorithm Abundant odd numbers step by step in the CLU programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Abundant odd numbers step by step in the CLU 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 CLU programming language
Source code in the clu programming language
% Integer square root
isqrt = proc (s: int) returns (int)
x0: int := s / 2
if x0 = 0 then
return(s)
else
x1: int := (x0 + s/x0) / 2
while x1 < x0 do
x0 := x1
x1 := (x0 + s/x0) / 2
end
return(x0)
end
end isqrt
% Calculate aliquot sum (for odd numbers only)
aliquot = proc (n: int) returns (int)
sum: int := 1
for i: int in int$from_to_by(3, isqrt(n)+1, 2) do
if n//i = 0 then
j: int := n / i
sum := sum + i
if i ~= j then
sum := sum + j
end
end
end
return(sum)
end aliquot
% Generate abundant odd numbers
abundant_odd = iter (n: int) yields (int)
while true do
if n < aliquot(n) then yield(n) end
n := n + 2
end
end abundant_odd
start_up = proc ()
po: stream := stream$primary_output()
count: int := 0
for n: int in abundant_odd(1) do
count := count + 1
if count <= 25 cor count = 1000 then
stream$putl(po, int$unparse(count)
|| ":\t"
|| int$unparse(n)
|| "\taliquot: "
|| int$unparse(aliquot(n)))
if count = 1000 then break end
end
end
for n: int in abundant_odd(1000000001) do
stream$putl(po, "First above 1 billion: "
|| int$unparse(n)
|| " aliquot: "
|| int$unparse(aliquot(n)))
break
end
end start_up
You may also check:How to resolve the algorithm Generator/Exponential step by step in the OCaml programming language
You may also check:How to resolve the algorithm Empty program step by step in the 11l programming language
You may also check:How to resolve the algorithm Gaussian elimination step by step in the VBA programming language
You may also check:How to resolve the algorithm Hailstone sequence step by step in the R programming language
You may also check:How to resolve the algorithm URL encoding step by step in the V (Vlang) programming language