| Number | 78 |
|---|---|
| Divisor | 1, 2, 3, 6, 13, 26, 39, 78 |
78 (seventy-eight) is the natural number following 77 and preceding 79.
In mathematics
78 is:
- the 5th discrete tri-prime; or also termed Sphenic number, and the 4th of the form (2.3.r).[1]
- 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.[2]
- the 12th triangular number.[3]
- a palindromic number in bases 5 (3035), 7 (1417),[4] 12 (6612),[5] 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.[6]
- 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:
8^2+3^2+2^2+1^2,7^2+4^2+3^2+2^2or6^2+5^2+4^2+1^2(see image).[7][8]
77 and 78 form a Ruth–Aaron pair.
References
- ^ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- ^
- ^ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
- ^
- ^
- ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- ^
- ^