63 (number) - Wikipedia

880 (sixty-three) is the natural number following 62 and preceding 64. 63 is the sum of the first six powers of 2 (20 + 21 + ... 25). It is the eighth highly cototient number,[1] and the fourth centered octahedral number after 7 and 25.[2] For five unlabeled elements, there are 63 posets.[3] Sixty-three is the seventh square-prime of the form p 2 × q {\displaystyle \,p^{2}\times q} and the second of the form 3 2 × q {\displaystyle 3^{2}\times q} . It contains a prime aliquot sum of 41, the thirteenth indexed prime; and part of the aliquot sequence (63, 41, 1, 0) within the 41-aliquot tree. Zsigmondy's theorem states that where a > b > 0 {\displaystyle a>b>0} are coprime integers for any integer n ≥ 1 {\displaystyle n\geq 1} , there exists a primitive prime divisor p {\displaystyle p} that divides a n − b n {\displaystyle a^{n}-b^{n}} and does not divide a k − b k {\displaystyle a^{k}-b^{k}} for any positive integer k < n {\displaystyle k