78 (number)

In mathematics

78 is:

the 5th discrete tri-prime; or also termed Sphenic number, and the 4th of the form (2.3.r).<ref>Template:Cite web</ref>
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.<ref>Template:Cite OEIS</ref>
the 12th triangular number.<ref>Template:Cite web</ref>
a palindromic number in bases 5 (303₅), 7 (141₇),<ref>Template:Cite OEIS</ref> 12 (66₁₂),<ref>Template:Cite OEIS</ref> 25 (33₂₅), and 38 (22₃₈).
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.<ref>Template:Cite web</ref>
the dimension of the exceptional Lie group E₆ 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).<ref>Template:Cite OEIS</ref><ref>Template:Cite OEIS</ref>

77 and 78 form a Ruth–Aaron pair.