Calculate \(\lfloor \sqrt 1 \rfloor + \lfloor \sqrt 2 \rfloor + \lfloor \sqrt 3 \rfloor + \cdots + \lfloor \sqrt {145} \rfloor\)
Note: \(\lfloor x \rfloor\) denotes the floor function
As follows:
1*3+2*5+3*7+4*9+5*11+6*13+7*15+8*17+9*19+10*21+11*23+12*2 = 1102
i.e. there are 3 ones, 5 twos, 7 threes, ... 23 elevens and 2 twelves.
