Question 1161108
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<pre>

Write all consecutive integer numbers 1, 2, 3, 4, 5 and so on, until, let say, 100.


From this sequence, erase perfect cubes and perfect squares

    1, 4, 8, 9, 16, 25, 27, 36, 49, 64, 81, 100.


In all, you will erase 12 terms;  11 of them are less than or equal to 81.


Now you can easily understand that the 75-th term of your sequence is the number 86,  


   +----------------------------------------------------------------------------+
   |   because 86 original terms  MINUS  11 erased terms = 75 remaining terms.  |
   +----------------------------------------------------------------------------+



<U>ANSWER</U>.  The 75-th term of your sequence is the number 86.
</pre>

Solved.


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It is a good problem for &nbsp;4-th - 5-th &nbsp;grade kids, &nbsp;of the <U>Math circle</U> &nbsp;or &nbsp;<U>Math Olympiad</U> level 

at a school or local University.


First, &nbsp;it teaches to think;

second, &nbsp;it teaches on how to find an idea;

third, &nbsp;it teaches to organize your thoughts;

fourth, &nbsp;it teaches to &nbsp;EXPRESS &nbsp;your thoughts;

fifth, &nbsp;it teaches that even Math problem, &nbsp;which seems to be tedious, &nbsp;can be solved and made as sweet as a cookie &nbsp;(!)


Come again to the forum soon to learn something new from me &nbsp;(!)



Bring nice problems with you &nbsp;(!)