How to resolve the algorithm Chowla numbers step by step in the XPL0 programming language

Published on 12 May 2024 09:40 PM
#Xpl0

How to resolve the algorithm Chowla numbers step by step in the XPL0 programming language

Table of Contents

Problem Statement

Chowla numbers are also known as:

The chowla number of   n   is   (as defined by Chowla's function):

The sequence is named after   Sarvadaman D. S. Chowla,   (22 October 1907 ──► 10 December 1995), a London born Indian American mathematician specializing in number theory.

German mathematician Carl Friedrich Gauss (1777─1855) said:

Chowla numbers can also be expressed as:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Chowla numbers step by step in the XPL0 programming language

Source code in the xpl0 programming language

func Chowla(N);         \Return sum of divisors
int  N, Div, Sum, Quot;
[Div:= 2;  Sum:= 0;
loop    [Quot:= N/Div;
        if Quot < Div then quit;
        if Quot = Div and rem(0) = 0 then \N is a square
            [Sum:= Sum+Quot;  quit];
        if rem(0) = 0 then
            Sum:= Sum + Div + Quot;
        Div:= Div+1;
        ];
return Sum;
];

int N, C, P;
[for N:= 1 to 37 do
    [IntOut(0, N);  Text(0, ": ");
    IntOut(0, Chowla(N));  CrLf(0);
    ];
C:= 1;  \count 2 as prime
N:= 3;  \only check odd numbers
repeat  if Chowla(N) = 0 then \N is prime
            C:= C+1;
        case N+1 of 100, 1000, 10_000, 100_000, 1_000_000, 10_000_000:
            [Text(0, "There are ");  IntOut(0, C);  Text(0, " primes < ");
            IntOut(0, N+1);  CrLf(0)]
        other [];
        N:= N+2;
until   N >= 10_000_000;
P:= 1;  \perfect numbers are of form: 2^(P-1) * (2^P - 1)
loop    [P:= P*2;
        N:= P*(P*2-1);
        if N > 35_000_000 then quit;
        if Chowla(N) = N-1 then \N is perfect
            [IntOut(0, N);  CrLf(0)];
        ];
]

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