76 (number)

← 75 76 77 →
← 70 71 72 73 74 75 76 77 78 79 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seventy-six
Ordinal	76th (seventy-sixth)
Factorization	2^2 × 19
Divisors	1, 2, 4, 19, 38, 76
Greek numeral	ΟϚ´
Roman numeral	LXXVI
Binary	10011002
Ternary	22113
Senary	2046
Octal	1148
Duodecimal	6412
Hexadecimal	4C16

76 (seventy-six) is the natural number following 75 and preceding 77.

In mathematics

76 is:

• a composite number; a square-prime, of the form (p², q) where q is a higher prime. It is the ninth of this general form and the seventh of the form (2².q).

• a Lucas number.^[1]
• a telephone or involution number, the number of different ways of connecting 6 points with pairwise connections.^[2]
• a nontotient.^[3]
• a 14-gonal number.^[4]
• a centered pentagonal number.^[5]
• an Erdős–Woods number since it is possible to find sequences of 76 consecutive integers such that each inner member shares a factor with either the first or the last member.^[6]
• with an aliquot sum of 64; within an aliquot sequence of two composite numbers (76,64,63,1,0) to the Prime in the 63-aliquot tree.
• an automorphic number in base 10.^[7] It is one of two 2-digit numbers whose square, 5,776, and higher powers, end in the same two digits. The other is 25.

There are 76 unique compact uniform hyperbolic honeycombs in the third dimension that are generated from Wythoff constructions.

In science

• The atomic number of osmium.
• The Little Dumbbell Nebula in the constellation Pegasus is designated as Messier object 76 (M76).

In other fields

The Bennington Flag features the number 76.

Seventy-six is also:

• In colloquial American parlance, reference to 1776, the year of the signing of the United States Declaration of Independence.
• Seventy-Six, an 1823 novel by American writer John Neal.
• The Spirit of '76, patriotic painting by Archibald MacNeal Willard.
• A brand of ConocoPhillips gas stations, 76.
• The number of trombonists leading the parade in "Seventy-Six Trombones", from Meredith Willson's musical The Music Man.
• The 76ers, a professional basketball team based in Philadelphia.
• 76, the debut album of Dutch trance producer and DJ Armin van Buuren.
• Years like 1876 and 1976
• Fallout 76, a 2018 game by Bethesda Studios.

See also

• List of highways numbered 76

References

1. "Sloane's A000032 : Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
2. "Sloane's A000085 : Involution numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-12-03.
3. "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
4. "Sloane's A051866 : 14-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
5. "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
6. "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
7. "Sloane's A003226 : Automorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.