232 (number)

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

← 231 232 233 →
Cardinaltwo hundred thirty-two
(two hundred thirty-second)
Factorization23 × 29
Greek numeralΣΛΒ´
Roman numeralCCXXXII
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]


  1. Sloane, N. J. A., ed. "Sequence A000124 (Central polygonal numbers (the Lazy Caterer's sequence))". OEIS Foundation. https://oeis.org/A000124. 
  2. Sloane, N. J. A., ed. "Sequence A000125 (Cake numbers)". OEIS Foundation. https://oeis.org/A000125. 
  3. Sloane, N. J. A., ed. "Sequence A001107 (10-gonal (or decagonal) numbers)". OEIS Foundation. https://oeis.org/A001107. 
  4. Sloane, N. J. A., ed. "Sequence A069125 (Centered 11-gonal numbers)". OEIS Foundation. https://oeis.org/A069125. .
  5. Sloane, N. J. A., ed. "Sequence A033950 (Refactorable numbers: number of divisors of n divides n)". OEIS Foundation. https://oeis.org/A033950. 
  6. Sloane, N. J. A., ed. "Sequence A005043 (Motzkin sums)". OEIS Foundation. https://oeis.org/A005043. 
  7. Sloane, N. J. A., ed. "Sequence A000926 (Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers))". OEIS Foundation. https://oeis.org/A000926. 
  8. Sloane, N. J. A., ed. "Sequence A005278 (Noncototients)". OEIS Foundation. https://oeis.org/A005278. 
  9. Sloane, N. J. A., ed. "Sequence A000085 (Number of self-inverse permutations on n letters, also known as involutions)". OEIS Foundation. https://oeis.org/A000085. 
  10. Peart, Paul; Woan, Wen-Jin (2000), "Generating functions via Hankel and Stieltjes matrices", Journal of Integer Sequences 3 (2): Article 00.2.1, http://www.emis.ams.org/journals/JIS/VOL3/PEART/peart1.pdf .
  11. Sloane, N. J. A., ed. "Sequence A007123 (Number of connected unit interval graphs with n nodes)". OEIS Foundation. https://oeis.org/A007123. 
  12. Sloane, N. J. A., ed. "Sequence A036679 (n^n - n!)". OEIS Foundation. https://oeis.org/A036679. 

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