← 176 177 178 →
Cardinalone hundred seventy-seven
Ordinal177th
(one hundred seventy-seventh)
Factorization3 × 59
Divisors1, 3, 59, 177
Greek numeralΡΟΖ´
Roman numeralCLXXVII
Binary101100012
Ternary201203
Senary4536
Octal2618
Duodecimal12912

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]

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

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

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]

The year AD 177 or 177 BC

## 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]

## References

1. ^ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ Sloane, N. J. A. (ed.). "Sequence A001358 (Semiprimes (or biprimes): products of two primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
3. ^ a b Sloane, N. J. A. (ed.). "Sequence A006881 (Squarefree semiprimes: Numbers that are the product of two distinct primes.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
4. ^ a b
5. ^ Sloane, N. J. A. (ed.). "Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
6. ^ Sloane, N. J. A. (ed.). "Sequence A016105 (Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
7. ^ Madachy, Joseph S. (1979). "Chapter 4: Magic and Antimagic Squares". Madachy's Mathematical Recreations. Mineola, NY: Dover. p. 95. ISBN 9780486237626. OCLC 5499643. S2CID 118826937.
8. ^ Sloane, N. J. A. (ed.). "Sequence A164843 (The smallest magic constant of an n X n magic square with distinct prime entries.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
9. ^ Sloane, N. J. A. (ed.). "Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
10. ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
11. ^ Sloane, N. J. A. (ed.). "Sequence A006450 (Prime-indexed primes: primes with prime subscripts.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
12. ^ Sloane, N. J. A. (ed.). "Sequence A249911 (60–gonal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
13. ^ Sloane, N. J. A. (ed.). "Sequence A002827 (Unitary perfect numbers: numbers k such that usigma(k) - k equals k.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
14. ^ Sloane, N. J. A. (ed.). "Sequence A001595 (Leonardo numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
15. ^ Sloane, N. J. A. (ed.). "Sequence A001383 (Number of n-node rooted trees of height at most 3)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
16. ^ Sloane, N. J. A. (ed.). "Sequence A000664 (Number of graphs with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
17. ^
18. ^ "Pub quiz". Tes Magazine. February 9, 2007. Retrieved 2022-06-27.