232 (number) explained

232 (two hundred [and] thirty-two) is the natural number following 231 and preceding 233.

In mathematics

Number:	232
Prime:	no

232 is both a central polygonal number^[1] and a cake number.^[2] It is both a decagonal number^[3] and a centered 11-gonal number.^[4] It is alsoa refactorable number,^[5] a Motzkin sum,^[6] an idoneal number,^[7] a Riordan number and a noncototient.^[8]

232 is a telephone number: in a system of seven telephone users, there are 232 different ways of pairing up some of the users.^{[9] [10]} There are also exactly 232 different eight-vertex connected indifference graphs, and 232 bracelets with eight beads of one color and seven of another.^[11] Because this number has the form, it follows that there are exactly 232 different functions from a set of four elements to a proper subset of the same set.^[12]

Notes and References

1. Central polygonal numbers (the Lazy Caterer's sequence).
2. Cake numbers.
3. 10-gonal (or decagonal) numbers.
4. Centered 11-gonal numbers. .
5. Refactorable numbers: number of divisors of n divides n.
6. Motzkin sums.
7. Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers).
8. Noncototients.
9. Number of self-inverse permutations on n letters, also known as involutions.
10. .
11. Number of connected unit interval graphs with n nodes.
12. n^n - n!.