177 (number)

Template:For Template:Infobox 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

$$177=2^7+7^2.$$

The fifty-seventh semiprime is 177 (after the square of 13), and it is the fifty-first semiprime with distinct prime factors.Template:Efn

The magic constant $M$ of the smallest full $3\times 3$ magic square consisting of distinct primes is 177:Template:Efn

47	89	101
113	59	5
17	29	71

Where the central cell $59=\frac{177}{3}$ represents the seventeenth prime number, and seventh super-prime; equal to the sum of all prime numbers up to 17, including one: $1+2+3+5+7+11+13+17=59.$

177 is also an arithmetic number, whose ${\sigma }_0$ holds an integer arithmetic mean of $60$ — it is the one hundred and nineteenth indexed member in this sequence, where $59+60=119.$ The first non-trivial 60-gonal number is 177.Template:Efn

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.