91 (number)

In mathematics

91 is:

• the twenty-seventh distinct semiprime and the second of the form (7.q), where q is a higher prime.
• the aliquot sum of 91 is 21; 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).
• the 13th triangular number.
• a hexagonal number, one of the few such numbers to also be a centered hexagonal number.
• a centered nonagonal number.
• a centered cube number.
• a square pyramidal number, being the sum of the squares of the first six integers.
• 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 .
• a repdigit in base 9 (1119).
• palindromic in bases 3 (101013), 9 (1119), and 12 (7712).
• a Riordan number.
• the smallest number that looks prime but is not, proven using the Rotten Theorem by John Conway.

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

In science

• McCarthy 91 function, a recursive function in discrete mathematics

References

References

1. {{Cite OEIS
2. "A000217 - OEIS".
3. "Sloane's A000384 : Hexagonal numbers". OEIS Foundation.
4. "Sloane's A003215 : Hex (or centered hexagonal) numbers". OEIS Foundation.
5. "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". OEIS Foundation.
6. "Sloane's A005898 : Centered cube numbers". OEIS Foundation.
7. "Sloane's A000330 : Square pyramidal numbers". OEIS Foundation.
8. {{cite OEIS. A047696. Smallest positive number that can be written in n ways as a sum of two (not necessarily positive) cubes.
9. Friedman, Erich. [http://www.stetson.edu/~efriedma/numbers.html What's Special About This Number?] {{Webarchive. link. (2018-02-23)
10. "Sloane's A005043 : Riordan numbers". OEIS Foundation.
11. (31 December 2020). "John Conway proves that 91 is the smallest number which looks prime but isn't". Ryan Andersen.
12. (9 May 2024). "Prime Numbers".