Concept

# 33 (number)

Summary
33 (thirty-three) is the natural number following 32 and preceding 34. In mathematics 33 is:
• specifically, the 8th distinct Semiprime, it being the 3rd of the form (3.q) where q is a higher prime.
• the largest positive integer that cannot be expressed as a sum of different triangular numbers.
• the smallest odd repdigit that is not a prime number.
• the sum of the first four positive factorials.
• the sum of the sum of the divisors of the first six positive integers.
• the sum of three cubes: 33=8866128975287528^{3}+(-8778405442862239)^{3}+(-2736111468807040)^{3}.
• equal to the sum of the squares of the digits of its own square in bases 9, 16 and 31. ** For numbers greater than 1, this is a rare property to have in more than one base.
• the smallest integer such that it and the next two integers all have the same number of divisors.
• the first member of the first cluster of three semiprimes 33, 34, 35; the next such cluster is 85, 86, 87.
• with an aliquot
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