232 (number)

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

231 232 233
Cardinal two hundred thirty-two
Ordinal 232nd
(two hundred and thirty-second)
Factorization 23× 29
Prime no
Roman numeral CCXXXII
Binary 111010002
Ternary 221213
Quaternary 32204
Quinary 14125
Senary 10246
Octal 3508
Duodecimal 17412
Hexadecimal E816
Vigesimal BC20
Base 36 6G36

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's A000124 : Central polygonal numbers (the Lazy Caterer's sequence)", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. "Sloane's A000125 : Cake numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. "Sloane's A001107 : 10-gonal (or decagonal) numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. "Sloane's A069125 : Centered 11-gonal numbers", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  5. "Sloane's A033950 : Refactorable numbers: number of divisors of n divides n", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. "Sloane's A005043 : Motzkin sums", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  7. "Sloane's A000926 : Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers)", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  8. "Sloane's A005278 : Noncototients", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. "Sloane's A000085 : Number of self-inverse permutations on n letters, also known as involutions", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  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. "Sloane's A007123 : Number of connected unit interval graphs with n nodes", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  12. "Sloane's A036679 : n^n - n!", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.