- Source: 177 (number)
177 (one hundred [and] seventy-seven) is the natural number following 176 and preceding 178.
In mathematics
One hundred and seventy-seven is the ninth Leyland number, where
177
=
2
7
+
7
2
.
{\displaystyle 177=2^{7}+7^{2}.}
The fifty-seventh semiprime is 177 (after the square of 13), and it is the fifty-first semiprime with distinct prime factors.
The magic constant
M
{\displaystyle M}
of the smallest full
3
×
3
{\displaystyle 3\times 3}
magic square consisting of distinct primes is 177:
Where the central cell
59
=
177
3
{\displaystyle {\text{ }}59={\tfrac {177}{3}}{\text{ }}}
represents the seventeenth prime number, and seventh super-prime; equal to the sum of all prime numbers up to 17, including one:
1
+
2
+
3
+
5
+
7
+
11
+
13
+
17
=
59.
{\displaystyle 1+2+3+5+7+11+13+17=59.}
177 is also an arithmetic number, whose
σ
0
{\displaystyle \sigma _{0}}
holds an integer arithmetic mean of
60
{\displaystyle 60}
— it is the one hundred and nineteenth indexed member in this sequence, where
59
+
60
=
119.
{\displaystyle {\text{ }}59+60=119.}
The first non-trivial 60-gonal number is 177.
177 is the tenth Leonardo number, part of a sequence of numbers closely related to the Fibonacci numbers.
In graph enumeration, there are
177 rooted trees with 10 nodes and height at most 3,
177 undirected graphs (not necessarily connected) that have 7 edges and no isolated vertices.
There are 177 ways of re-connecting the (labeled) vertices of a regular octagon into a star polygon that does not use any of the octagon edges.
In other fields
177 is the second highest score for a flight of three darts, below the highest score of 180.
See also
The year AD 177 or 177 BC
Notes
References
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