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Q: What numbers that have an odd number of factors and are less than 101?

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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.

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There are 31 numbers less than 1,000 which have an odd number of factors. They are: 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961.

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The numbers for which the sum of its proper factors is 1 less than the number is the powers of 2; less than 50 these are: 2, 4, 8, 16 & 32.

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