11. In 1-100, what is the sum of all natural numbers with only three divisors?

11. In 1-100, what is the sum of all natural numbers with only three divisors?

There are only four numbers, about three
2x2,3x3,5x5,7x7,
The sum of them is 4 + 9 + 25 + 49 = 87

Among the natural numbers from 1 to 100, () has the most divisors
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It should be 60 and 96, they each have 12 divisors
60 = 2 ^ 2 times 3 times 5, so the divisor has the product of each exponent plus 1, that is, (2 + 1) * (1 + 1) * (1 + 1) = 12
96 = 2 ^ 5 times 3, so the divisor is also the product of each index plus 1, that is, (5 + 1) * (1 + 1) = 12

Try to find all natural numbers with 10 divisors within 100

If the number within 100 is divided into prime number ^ 4 times 1, then it is 10 factors
2*2*2*2*3=48 2^4 *3^1=48 (4+1)*(1+1)=10
2*2*2*2*5=80 2^4*5^1=80 (4+1)*(1+1)=10
Therefore, the natural number with 10 divisors within 100 is 48 80