time complexity

Question

i am getting t.c as O(n^5) but given answer as O(n^4) what should be the answer

Answer 1

$\sum_{i=1}^{n} \sum_{j=1}^{i^{2}} j/2 = O(n^{5})$

Please suggest accordingly

Answer 2

It think it's O(n⁴) because 

i will run n times

j will go till n² but it will be running only n times as from 1 to n² you will have n cases when j%i will be 0. For eg. say n=12 iteration is going on. n² is 144. Now from 1 to 144, you will encounter 12 (n) cases like 12,24,36,48,etc. 

Coming to k, k goes till j and hence can go till n² as value of j will go till n²

so n*n*n² = n⁴

Answer 3

For i=1 ,j=1,k=1

for i=2 ,j=1 to 4 ,k=2+4=1(1+2)

for i=3,j=1 to 9 , k=3+6+9=3(1+2+3)

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.overall summation = 1+2(1+2)+3(1+2+3)+.....+n(1+2+3+....+n)

=1.1+2.o(2^2)+3.o(3^2)+.....n.o(n2)

=summation of cubic series=o(n^4)