91 (number)
91 is the natural number following 90 and preceding 92.
In mathematics
91 is:- the twenty-seventh distinct semiprime and the second of the form, where q is a higher prime.
- the aliquot sum of 91 is 21; itself a semiprime, within an aliquot sequence of two composite numbers to the prime in the 11-aliquot tree. 91 is the fourth composite number in the 11-aliquot tree..
- 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 :
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:
- the smallest pseudoprime satisfying the congruence.
- a repdigit in base 9.
- palindromic in bases 3, 9, and 12.
- a Riordan number.
- the smallest number that looks prime but is not, proven using the Rotten Theorem by John Conway.