MathDB

You are initially given the number

n=1

. Each turn, you may choose any positive divisor

d\mid n

, and multiply

n

d+1

. For instance, on the first turn, you must select

d=1

, giving

n=1\cdot(1+1)=2

as your new value of

n

. On the next turn, you can select either

d=1

2

, giving

n=2\cdot(1+1)=4

n=2\cdot(2+1)=6

, respectively, and so on.
Find an algorithm that, in at most

k

steps, results in

n

being divisible by the number

2021^{2021^{2021}} - 1

.
An algorithm that completes in at most

k

steps will be awarded:
1 pt for

k>2021^{2021^{2021}}

20 pts for

k=2021^{2021^{2021}}

50 pts for

k=10^{10^4}

75 pts for

k=10^{10}

90 pts for

k=10^5

95 pts for

k=6\cdot10^4

100 pts for

k=5\cdot10^4

2