Question

the sum of the number of factors of the number N anN^2 is 34. how many such distinct numbers N<150 exist
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Answer 1

Step-by-step explanation:

Lets take an example 12. Factors of 12 are 2- 2time and 3- 1 time. Total no of factor - (2+1) * (1+1) =6.

For 12*12 - it has 2 - 4times and 3 - 2 timed. Total no of factor - 5*3=15

Case 1 :-

N=x.y

For N*N

Trying reverse approach. 35 = 5*7.

Factors are x - 4times and y- 6times.

FOR N - x -2 times and y- 3 times.

Total no of factor is (2+1)*(3+1)=12

Case 2:-

If N^2 is raised to the power of 34.

N^2 will have 34 factors.

And hence for N we have 17 factors.

Hence total no of factor as 17+1 = 18