213 (number)
213 (two hundred [and] thirteen) is the number following 212 and preceding 214.
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| Cardinal | two hundred thirteen | |||
| Ordinal | 213th (two hundred thirteenth) | |||
| Factorization | 3 × 71 | |||
| Divisors | 1, 3, 71, 213 | |||
| Greek numeral | ΣΙΓ´ | |||
| Roman numeral | CCXIII | |||
| Binary | 110101012 | |||
| Ternary | 212203 | |||
| Octal | 3258 | |||
| Duodecimal | 15912 | |||
| Hexadecimal | D516 | |||
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
- 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.
- Sloane, N. J. A. (ed.). "Sequence A011784 (Levine's sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- Guy, Richard K. (April 1998). "What's left?". Math Horizons. 5 (4): 5–7. JSTOR 25678158.
- 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.
- 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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