In Mathematics
32 is the smallest number n with exactly 7 solutions to the equation φ(x) = n. It is also the sum of the totient function for the first ten integers.
The fifth power of two, 32 is also a Leyland number since 24 + 42 = 32.
As with every power of two, 32 has an aliquot sum one less than itself: the prime 31. 32 is the first member of the 31-aliquot tree.
32 is the ninth happy number.
32 = 11 + 22 + 33
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“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)