87 (number)

← 86 87 88 →
← 80 81 82 83 84 85 86 87 88 89 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	eighty-seven
Ordinal	87th (eighty-seventh)
Factorization	3 × 29
Divisors	1, 3, 29, 87
Greek numeral	ΠΖ´
Roman numeral	LXXXVII, lxxxvii
Binary	10101112
Ternary	100203
Senary	2236
Octal	1278
Duodecimal	7312
Hexadecimal	5716

87 (eighty-seven) is the natural number following 86 and preceding 88.

In mathematics

87 is:

• the sum of the squares of the first four primes (87 = 2² + 3² + 5² + 7²).
• the sum of the sums of the divisors of the first 10 positive integers. ^[1]
• the thirtieth semiprime, ^[2] and the twenty-sixth distinct semiprime ^[3] and the eighth of the form (3.q).
• together with 85 and 86, ^[4] forms the last semiprime in the 2nd cluster of three consecutive semiprimes; the first comprising 33, 34, 35.
• with an aliquot sum of 33; itself a semiprime, within an aliquot sequence of five composite numbers (87,33,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
• 5! - 4! - 3! - 2! - 1! = 87
• the last two decimal digits of Graham's number.

In sports

• Cricket in Australia holds 87 as a superstitiously unlucky score and is referred to as "the devil's number". This originates from the fact that 87 is 13 runs short of a century. 187, 287, and so on are also considered unlucky but are not as common as 87 on its own. ^[5]

In other fields

Eighty-seven is also:

• The opus number of the 24 Preludes and Fugues of Dmitri Shostakovich.
• In model railroading, the ratio of the popular H0 scale is 1:87. ^[6] Proto:87 scale claims to offer precise proportions of wheels and tracks of real railroads.
• 87 is by far the most commonly used octane rating of gasoline in the United States, Canada, Australia, and New Zealand.

References

1. Sloane, N. J. A. (ed.). "SequenceA024916(sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. "A001358 - OEIS". oeis.org. Retrieved 2020-08-10.
3. "A006881 - OEIS". oeis.org. Retrieved 2020-08-10.
4. Sloane, N. J. A. (ed.). "SequenceA056809". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Ferris, Sam (2014-11-02). "The real story behind Australia's unlucky number 87". cricket.com.au. Retrieved 2022-01-27.
6. "Guide to model railroading scales and gauges". Model Railroader . 2 November 2011. Archived from the original on 22 June 2015. Retrieved 2 October 2016.