1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
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There are 12 numbers less than 150 which have an odd number of factors: 1,4,9,16,25,36,49,64,81,100,121,144.
150 = 12 + 62 + 72 + 82
250 of 44 is much greater than 150.
151
Just calculate the square of 1, the square of 2, etc.