32 (thirty-two) is the natural number following 31 and preceding 33.
Mathematics
32 is the fifth power of two (<math>2^{5}</math>), making it the first non-unitary fifth-power of the form <math>p^{5}</math> where <math>p</math> is prime. 32 is the totient summatory function <math>\Phi(n)</math> over the first 10 integers, and the smallest number <math>n</math> with exactly 7 solutions for <math>\varphi (n)</math>.
The aliquot sum of a power of two is always one less than the number itself, therefore the aliquot sum of 32 is 31.
<math display=block>
\begin{align}
32 & = 1^{1} + 2^{2} + 3^{3} \\
32 & = (1\times4)+(2\times5)+(3\times6) \\
32 & = (1\times2)+(1\times2\times3)+(1\times2\times3\times4) \\
32 & = (1\times2\times3)+(4\times5)+(6)
\end{align}</math>
The product between neighbor numbers of 23, the dual permutation of the digits of 32 in decimal, is equal to the sum of the first 32 integers: <math>22 \times 24= 528</math>.