歐拉計劃(python) problem 29

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Distinct powersProblem 29

Consider all integer combinations of ab for 2 ≤ a ≤ 5 and 2 ≤ b ≤ 5:

22=4, 23=8, 24=16, 25=32
32=9, 33=27, 34=81, 35=243
42=16, 43=64, 44=256, 45=1024
52=25, 53=125, 54=625, 55=3125

If they are then placed in numerical order, with any repeats removed, we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by ab for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100?

python code:

aindex=[i for i in range(2,101)]bindex=[2 for i in range(2,101)]value=[i*i for i in range(2,101)]count=0while len(value)>0:    pointValue=min(value)    count+=1    for i in range(len(value)-1,-1,-1):        if value[i]==pointValue:            if bindex[i]==100:                del aindex[i],bindex[i],value[i]            else:                bindex[i]+=1                value[i]*=aindex[i]print(count)

time: <1s

歐拉計劃(python) problem 29