# 78 (number)

(Redirected from Seventy-eight)
 ← 77 78 79 →
Cardinalseventy-eight
Ordinal78th
(seventy-eighth)
Factorization2 × 3 × 13
Divisors1, 2, 3, 6, 13, 26, 39, 78
Greek numeralΟΗ´
Roman numeralLXXVIII
Binary10011102
Ternary22203
Senary2106
Octal1168
Duodecimal6612

78 (seventy-eight) is the natural number following 77 and followed by 79.

## In mathematics

78 is:

• the 4th 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 33; 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 (3035), 7 (1417), 12 (6612), 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.[2]
• 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: ${\displaystyle 8^{2}+3^{2}+2^{2}+1^{2}}$, ${\displaystyle 7^{2}+4^{2}+3^{2}+2^{2}}$ or ${\displaystyle 6^{2}+5^{2}+4^{2}+1^{2}}$ (see image).[3][4]

77 and 78 form a Ruth–Aaron pair.

78 is also:

## References

1. ^ "Sloane's A007304 : Sphenic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
2. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
3. ^
4. ^