Not A Perfect Number

6=1+2+328=1+2+4+7+146=21(221)28=22(231)\begin{array}{ll} 6 = 1 + 2 + 3 & 28 = 1 + 2 + 4 + 7 + 14 \\ 6 = 2^1\cdot (2^2 - 1) & 28 = 2^2\cdot (2^3 - 1) \end{array}

6 and 28 are perfect numbers, because each of them is equal to the sum of its proper divisors, as shown above. They are also numbers of the form 2n(2n+11)2^n\cdot (2^{n+1} - 1).

Not all numbers of the form 2n(2n+11)2^n\cdot (2^{n+1}-1) are perfect numbers. Let's call those numbers imperfect. For instance, 120 is an imperfect number because 120=23(241)120 = 2^3\cdot (2^4-1) yet 1201+2+3+4+5+6+8+10+12+15+20+24+30+40+60.120 \not= 1+2+3+4+5+6+8+10+12 \\ +15+20+24+30+40+60.

What is the smallest imperfect number greater than 120?

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