177 (number) explained

Number:	177
Divisor:	1, 3, 59, 177

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),^[1] and it is the fifty-first semiprime with distinct prime factors.^[2]

M of the smallest full 3 x 3 magic square consisting of distinct primes is 177:^{[3] [4]}

47	89	101
113	59	5
17	29	71

59 = \tfrac { 177 }{ 3 } represents the seventeenth prime number,^[5] and seventh super-prime;^[6] 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.

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.^[7]

See also

The year AD 177 or 177 BC

Notes and References

1. 2023-11-04 .
2. 2023-11-04 .
3. Book: Madachy, Joseph S. . Joseph Madachy . Madachy's Mathematical Recreations . Chapter 4: Magic and Antimagic Squares . Mineola, NY . . 1979 . 95 . 9780486237626 . 5499643 . 118826937 .
4. 2023-11-04 .
5. 2023-11-04 .
6. 2023-11-04 .
7. Pub quiz. Tes Magazine. February 9, 2007. 2022-06-27.