85 (number)
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85 (eighty-five) is the natural number following 84 and preceding 86.
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Cardinal | eighty-five | |||
Ordinal | 85th (eighty-fifth) | |||
Factorization | 5 × 17 | |||
Divisors | 1, 5, 17, 85 | |||
Greek numeral | ΠΕ´ | |||
Roman numeral | LXXXV, lxxxv | |||
Binary | 10101012 | |||
Ternary | 100113 | |||
Senary | 2216 | |||
Octal | 1258 | |||
Duodecimal | 7112 | |||
Hexadecimal | 5516 |
In mathematics
[edit]85 is:
- the product of two prime numbers (5 and 17), and is therefore a semiprime of the form (5.q) where q is prime.
- specifically, the 24th Semiprime, it being the fourth of the form (5.q).
- together with 86 and 87, forms the second cluster of three consecutive semiprimes; the first comprising 33, 34, 35.[1]
- with a prime aliquot sum of 23 in the short aliquot sequence (85,23,1,0).
- an octahedral number.[2]
- a centered triangular number.[3]
- a centered square number.[4]
- a decagonal number.[5]
- the smallest number that can be expressed as a sum of two squares, with all squares greater than 1, in two ways, 85 = 92 + 22 = 72 + 62.[6]
- the length of the hypotenuse of four Pythagorean triangles.
- a Smith number in decimal.[7]
In other fields
[edit]- The radix of the Ascii85 (sometimes called Base85) binary-to-text encoding
- Part of the assignation for the Toyota AE85, commonly referred to as an "eight-five".
References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A056809 (Numbers k such that k, k+1 and k+2 are products of two primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001844 (Centered square numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001107 (10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007692 (Numbers that are the sum of 2 non-zero squares in 2 or more ways)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.. The two smaller numbers on this list, 50 and 65, have 1 as one of the squares in their representations as sums of two squares.
- ^ Sloane, N. J. A. (ed.). "Sequence A006753 (Smith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
External links
[edit]Wikimedia Commons has media related to 85 (number).
- 85
- Jorge Stolfi, The Hollywood Constant.