## Tuesday, 5 March 2013

### TUESDAY, 5 MARCH 2013

Today is the $64^{th}$ day of the year.

$64 = 2^6$

$64 = 2^3 \times 2^3 = 8 \times 8$ which means that $64$ is a perfect square.

$64 = 2^2 \times 2^2 \times 2^2 = 4 \times 4 \times 4$ which means that $64$ is a perfect cube.

A sequence of numbers that are both squares and cubes would be:
$1, 64, 729, 4096, 15625, 531441, 244140625$ if I have calculated it correctly. Surprisingly, I cannot find this series at The On-Line Encyclopedia of Integer Sequences®.

Update
The reason I could not find it was because I had missed out three terms between $15625$ and $531441$, namely $46656, 117649, 262144$. With these included we get a match at A001014 (see the first comment).