78 (seventy-eight) is the natural number following 77 and preceding 79.
In mathematics
thumb|78 as the sum of four distinct nonzero squares
78 is:
- the 5th discrete tri-prime; or also termed Sphenic number, and the 4th of the form (2.3.r).
- an abundant number with an aliquot sum of 90; within an aliquot sequence of nine composite numbers (78, 90,144,259,45,33,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
- a semiperfect number, as a multiple of a perfect number.
- the 12th triangular number.
- a palindromic number in bases 5 (303<sub>5</sub>), 7 (141<sub>7</sub>), 12 (66<sub>12</sub>), 25 (33<sub>25</sub>), and 38 (22<sub>38</sub>).
- a Harshad number in bases 3, 4, 5, 6, 7, 13 and 14.
- an Erdős–Woods number, since it is possible to find sequences of 78 consecutive integers such that each inner member shares a factor with either the first or the last member.
- the dimension of the exceptional Lie group E<sub>6</sub> and several related objects.
- the smallest number that can be expressed as the sum of four distinct nonzero squares in more than one way: <math>8^2+3^2+2^2+1^2</math>, <math>7^2+4^2+3^2+2^2</math> or <math>6^2+5^2+4^2+1^2</math> (see image).
77 and 78 form a Ruth–Aaron pair.