# 232 (number)

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

 ← 231 232 233 →
Cardinaltwo hundred thirty-two
Ordinal232nd
(two hundred thirty-second)
Factorization23 × 29
Primeno
Greek numeralΣΛΒ´
Roman numeralCCXXXII
Binary111010002
Ternary221213
Quaternary32204
Quinary14125
Senary10246
Octal3508
Duodecimal17412
VigesimalBC20
Base 366G36

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 also a refactorable number,[5] a Motzkin sum,[6] an idoneal number,[7] 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 232 = 44 − 4!, it follows that there are exactly 232 different functions from a set of four elements to a proper subset of the same set.[12]

## References

1. ^ Sloane, N. J. A. (ed.). "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Sloane, N. J. A. (ed.). "Sequence A000125 (Cake numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ Sloane, N. J. A. (ed.). "Sequence A069125 (Centered 11-gonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
5. ^
6. ^ Sloane, N. J. A. (ed.). "Sequence A005043 (Motzkin sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. ^
8. ^ Sloane, N. J. A. (ed.). "Sequence A005278 (Noncototients)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
9. ^
10. ^ Peart, Paul; Woan, Wen-Jin (2000), "Generating functions via Hankel and Stieltjes matrices" (PDF), Journal of Integer Sequences, 3 (2), Article 00.2.1, MR 1778992.
11. ^
12. ^ Sloane, N. J. A. (ed.). "Sequence A036679 (n^n - n!)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.