78 (seventy-eight) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
77 and preceding
79.
In mathematics
78 is:
*the 5th discrete tri-prime; or also termed
Sphenic number
In number theory, a sphenic number (from , 'wedge') is a positive integer that is the product of three distinct prime numbers. Because there are infinitely many prime numbers, there are also infinitely many sphenic numbers.
Definition
A sphenic ...
, and the 4th of the form (2.3.r).
*an
abundant number
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total ...
with an
aliquot sum
In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself.
That is,
s(n)=\sum_ d \, .
It can be used to characterize the prime numbers, perfect numbers, sociabl ...
of
90; within an
aliquot sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
Def ...
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 triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots in ...
.
*a
palindromic number
A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palin ...
in bases 5 (303
5), 7 (141
7), 12 (66
12), 25 (33
25), and 38 (22
38).
*a
Harshad number
In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ...
in bases 3, 4, 5, 6, 7, 13 and 14.
*an
Erdős–Woods number
In number theory, a positive integer is said to be an Erdős–Woods number if it has the following property:
there exists a positive integer such that in the sequence of consecutive integers, each of the elements has a non-trivial common fac ...
, 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
Exception(s), The Exception(s), or exceptional may refer to:
Arts and entertainment
* '' The Exception'', a 2016 British film
* ''The Exception'' (2006 novel), a Danish novel (orig. ''Undtagelsen'', 2004) by Christian Jungersen
* ''The Excep ...
Lie group
E6 and several related objects.
*the smallest number that can be expressed as the sum of four distinct nonzero
squares
In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...
in more than one way:
,
or
(see image).
77 and 78 form a
Ruth–Aaron pair.
References
{{Integers, zero
Integers