213 (number)

← 212 213 214 →
Cardinaltwo hundred thirteen
Ordinal213th
(two hundred thirteenth)
Factorization3 × 71
Divisors1, 3, 71, 213
Greek numeralΣΙΓ´
Roman numeralCCXIII
Binary110101012
Ternary212203
Senary5536
Octal3258
Duodecimal15912
HexadecimalD516

213 (two hundred [and] thirteen) is the number following 212 and preceding 214.

In mathematics

213 and the other permutations of its digits are the only three-digit number whose digit sums and digit products are equal.[1] It is a member of the quickly-growing Levine sequence, constructed from a triangle of numbers in which each row counts the copies of each value in the row below it.[2][3]

As the product of the two distinct prime numbers 3 and 71, it is a semiprime, the first of a triple of three consecutive semiprimes 213, 214, and 215.[4] Its square, 2132 = 45369, is one of only 15 known squares that can be represented as a sum of distinct factorials.[5]

See also

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A034710 (Positive numbers for which the sum of digits equals the product of digits)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A011784 (Levine's sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Guy, Richard K. (April 1998). "What's left?". Math Horizons. 5 (4): 5–7. doi:10.1080/10724117.1998.11975052. JSTOR 25678158.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A039833 (Smallest of three consecutive squarefree numbers k, k+1, k+2 of the form p*q where p and q are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A014597 (Numbers k such that k^2 is a sum of distinct factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.


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