Chowla numbers: Difference between revisions
Added XPL0 example.
(Added XPL0 example.) |
|||
Line 5,252:
33,550,336 is a perfect number
There are 5 perfect numbers <= 35,000,000
</pre>
=={{header|XPL0}}==
<lang XPL0>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)];
];
]</lang>
{{out}}
<pre>
1: 0
2: 0
3: 0
4: 2
5: 0
6: 5
7: 0
8: 6
9: 3
10: 7
11: 0
12: 15
13: 0
14: 9
15: 8
16: 14
17: 0
18: 20
19: 0
20: 21
21: 10
22: 13
23: 0
24: 35
25: 5
26: 15
27: 12
28: 27
29: 0
30: 41
31: 0
32: 30
33: 14
34: 19
35: 12
36: 54
37: 0
There are 25 primes < 100
There are 168 primes < 1000
There are 1229 primes < 10000
There are 9592 primes < 100000
There are 78498 primes < 1000000
There are 664579 primes < 10000000
6
28
496
8128
33550336
</pre>
| |||