177 (number)

For other topics, see 177 (disambiguation).

177 (one hundred [and] seventy-seven) is the natural number following 176 and preceding 178.

← 176 177 178 →
← 170 171 172 173 174 175 176 177 178 179 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred seventy-seven
Ordinal	177th (one hundred seventy-seventh)
Factorization	3 × 59
Divisors	1, 3, 59, 177
Greek numeral	ΡΟΖ´
Roman numeral	CLXXVII, clxxvii
Binary	101100012
Ternary	201203
Senary	4536
Octal	2618
Duodecimal	12912
Hexadecimal	B116

In mathematics

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 fifty-first 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]

47	89	101
113	59	5
17	29	71

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]

Notes

1. Following the fifty-sixth member 166,^[3] whose divisors hold an arithmetic mean of 63,^[4] a value equal to the aliquot part of 177.^[5]
   As a semiprime of the form n = p × q for which p and q are distinct prime numbers congruent to 3 mod 4, 177 is the eleventh Blum integer, where the first such integer 21 divides the aliquot part of 177 thrice over.^[6]
2. The first three such magic constants of non-trivial magic squares with distinct prime numbers sum to 177 + 120 + 233 = 530 — also the sum between the first three perfect numbers, 6 + 28 + 496^[9] — that is one less than thrice 177.
3. Where 60 is the value of the second unitary perfect number, after 6.^[13]