177 (number)

One hundred and seventy-seven is the eighth Leyland number, where^[1]

$${\displaystyle 177=2^{7}+7^{2}.}$$

The fifty-seventh semiprime is 177 (after the square of 13),^[2] and it is the 51st semiprime with distinct prime factors.^[3][a]

The magic constant ${\displaystyle M}$ of the smallest full ${\displaystyle 3\times 3}$ magic square consisting of distinct primes is 177:^[7][8][b]

Where the central cell ${\displaystyle {\text{ }}59={\tfrac {177}{3}}{\text{ }}}$ represents the seventeenth prime number,^[10] and seventh super-prime;^[11] equal to the sum of all prime numbers up to 17, including one: ${\displaystyle 1+2+3+5+7+11+13+17=59.}$

177 is also an arithmetic number, whose ${\displaystyle \sigma _{0}}$ holds an integer arithmetic mean of ${\displaystyle 60}$ — it is the one hundred and nineteenth indexed member in this sequence,^[4] where ${\displaystyle {\text{ }}59+60=119.}$ The first non-trivial 60-gonal number is 177.^[12][c]

177 is the tenth Leonardo number, part of a sequence of numbers closely related to the Fibonacci numbers.^[14]

In graph enumeration, there are

• 177 rooted trees with 10 nodes and height at most 3,^[15]
• 177 undirected graphs (not necessarily connected) that have 7 edges and no isolated vertices.^[16]

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.^[17]