154 (one hundred
ndfifty-four) 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
153 and preceding
155.
In mathematics
154 is a
nonagonal number. Its factorization makes 154 a
sphenic number.
There is no integer with exactly 154 coprimes below it, making 154 a
noncototient
In number theory, a noncototient is a positive integer that cannot be expressed as the difference between a positive integer and the number of coprime integers below it. That is, , where stands for Euler's totient function
In number theory ...
, nor is there, in base 10, any integer that added up to its own digits yields 154, making 154 a
self number
154 is the sum of the first six
factorial
In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial:
\begin
n! &= n \times ...
s, if one starts with
and assumes that
.
With just 17 cuts, a pancake can be cut up into 154 pieces (
Lazy caterer's sequence).
The distinct prime factors of 154 add up to 20, and so do the ones of 153, hence the two form a
Ruth-Aaron pair. 154! + 1 is a
factorial prime
A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even).
The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are :
: 2 (0! + 1 or 1! + 1) ...
.
References
* Wells, D. ''
The Penguin Dictionary of Curious and Interesting Numbers'' London: Penguin Group. (1987): 140 - 141
External links
Virtual Science: Number 154
{{Integers, 1
Integers