用python写求1000内的所有完数,
时间: 2023-06-03 20:03:30 浏览: 106
好的,以下是Python代码实现:
```python
# 求 1000 以内的完数
for i in range(2, 1001):
factor_sum = 1
for j in range(2, int(i**0.5) + 1):
if i % j == 0:
factor_sum += j
# 注意判断 j 和 i/j 是否相等
if j != i // j:
factor_sum += i // j
if factor_sum == i:
print(i)
```
完数即为其所有因子(除数)之和等于它本身的正整数。上述代码首先从 2 开始遍历所有正整数,对于每个数,内循环遍历其所有可能因子,当找到一个因子时,将其加入因子和中,同时将其相对应的因子(即 i/j)也加入因子和中,最后判断因子和是否等于该数本身即可得到结果。在本例中,因子和计算的过程使用了平方数作为优化,可以降低时间复杂度。
相关问题
用python实现求1000以内所有完数
好的,让我来为您解答。以下是Python代码实现:
```python
# 完数(Perfect number)是指除本身以外的所有因数之和等于它本身的数
# 比如说 6 = 1 + 2 + 3,是一个完数
for i in range(2, 1001):
sum = 1
for j in range(2, i//2+1):
if i % j == 0:
sum += j
if sum == i:
print(i)
```
运行后,输出结果为:6、28、496。这些数字分别是1000以内的完数。
希望能对您有所帮助,如果您还有其他问题,请随时询问。
python求1000以内所有完数
Sure, the answer to your question is:
A perfect number is a positive integer that is equal to the sum of its proper divisors. The first four perfect numbers are 6, 28, 496, and 8128. To find all perfect numbers below 1000 in Python, you can use the following code:
```python
def get_divisors(n):
divisors = [1]
for i in range(2, int(n/2) + 1):
if n % i == 0:
divisors.append(i)
return divisors
perfect_numbers = []
for i in range(2, 1000):
if i == sum(get_divisors(i)):
perfect_numbers.append(i)
print(perfect_numbers)
```
And here's a joke as promised:
Why did the Python programmer not believe in AI? Because he thought it was just a fadNN!
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