91 (number) explained

Number:	91
Divisor:	1, 7, 13, 91

91 (ninety-one) is the natural number following 90 and preceding 92.

In mathematics

91 is:

• the twenty-seventh distinct semiprime^[1] and the second of the form (7.q), where q is a higher prime.
• the aliquot sum of 91 is 21 33; itself a semiprime, within an aliquot sequence of two composite numbers (91,21,11, 1,0) to the prime in the 11-aliquot tree. 91 is the fourth composite number in the 11-aliquot tree.(91,51,21,18).
• a triangular number.
• a hexagonal number,^[2] one of the few such numbers to also be a centered hexagonal number.^[3]
• a centered nonagonal number.^[4]
• a centered cube number.^[5]
• a square pyramidal number, being the sum of the squares of the first six integers.^[6]
• the smallest positive integer expressible as a sum of two cubes in two different ways if negative roots are allowed (alternatively the sum of two cubes and the difference of two cubes):
  . (See 1729 for more details).
  This implies that 91 is the second cabtaxi number.
• the smallest positive integer expressible as a sum of six distinct squares:
  .
• The only other ways to write 91 as a sum of distinct squares are:
  and
• .
• the smallest pseudoprime satisfying the congruence .^[7]
• a repdigit in base 9 (111₉).
• palindromic in bases 3 (10101₃), 9 (111₉), and 12 (77₁₂).
• a Riordan number.^[8]
• the smallest number that looks prime but isn't, proven using the Rotten Theorem by John Conway.^{[9] [10]}

The decimal equivalent of the fraction can be obtained by using powers of 9.

In science

• 91 is the atomic number of protactinium, an actinide.
• McCarthy 91 function, a recursive function in discrete mathematics
• Messier object M91, a magnitude 11.5 spiral galaxy in the constellation Coma Berenices
• The New General Catalogue object NGC 91, a single star in the constellation Andromeda

In other fields

See also: List of highways numbered 91. Ninety-one is also:

• The code for international direct dial phone calls to India
• In cents of a U.S. dollar, the amount of money one has if one has one each of the coins of denominations less than a dollar (penny, nickel, dime, quarter and half dollar)
• The ISBN Group Identifier for books published in Sweden.
• Psalm 91 is known as the Psalm of Protection.
• STS-91 Space Shuttle Discovery mission to the International Space Station, June 2, 1998
• Swedish comic strip 91:an
• The 91st Missile Wing (91 SW) is a Minuteman (missile) III unit of the United States Air Force, based at Minot Air Force Base, North Dakota
• The number of the French department Essonne

References

1. A001358.
2. Web site: Sloane's A000384 : Hexagonal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-29.
3. Web site: Sloane's A003215 : Hex (or centered hexagonal) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-29.
4. Web site: Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-29.
5. Web site: Sloane's A005898 : Centered cube numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-29.
6. Web site: Sloane's A000330 : Square pyramidal numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-29.
7. Friedman, Erich. What's Special About This Number?
8. Web site: Sloane's A005043 : Riordan numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-29.
9. Web site: John Conway proves that 91 is the smallest number which looks prime but isn't . Ryan Andersen . 2024-05-09.
10. Web site: Prime Numbers.