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^[1]

[math]\displaystyle{ 177 = 2^7 + 7^2. }[/math]

The fifty-seventh semiprime is 177 (after the square of 13),^[2] and it is the fifty-first semiprime with distinct prime factors.^{[3][lower-alpha 1]}

The magic constant [math]\displaystyle{ M }[/math] of the smallest full [math]\displaystyle{ 3 \times 3 }[/math] magic square consisting of distinct primes is 177:^{[7][8][lower-alpha 2]}

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

177 is also an arithmetic number, whose [math]\displaystyle{ \sigma_0 }[/math] holds an integer arithmetic mean of [math]\displaystyle{ 60 }[/math] — it is the one hundred and nineteenth indexed member in this sequence,^[4] where [math]\displaystyle{ \text { }59 + 60 = 119. }[/math] The first non-trivial 60-gonal number is 177.^{[12][lower-alpha 3]}

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]

In other fields

177 is the second highest score for a flight of three darts, below the highest score of 180.^[18]

See also

The year AD 177 or 177 BC

Notes

References

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