177 (number)

From HandWiki
Short description: Natural number
← 176 177 178 →
Cardinalone hundred seventy-seven
Ordinal177th
(one hundred seventy-seventh)
Factorization3 × 59
Divisors1, 3, 59, 177
Greek numeralΡΟΖ´
Roman numeralCLXXVII
Binary101100012
Ternary201203
Quaternary23014
Quinary12025
Senary4536
Octal2618
Duodecimal12912
HexadecimalB116
Vigesimal8H20
Base 364X36

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]

47 89 101
113 59 5
17 29 71

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

  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)". OEIS Foundation. https://oeis.org/A076980. 
  2. ↑ Sloane, N. J. A., ed. "Sequence A001358 (Semiprimes (or biprimes): products of two primes.)". OEIS Foundation. https://oeis.org/A001358. Retrieved 2023-11-04. 
  3. ↑ 3.0 3.1 Sloane, N. J. A., ed. "Sequence A006881 (Squarefree semiprimes: Numbers that are the product of two distinct primes.)". OEIS Foundation. https://oeis.org/A006881. Retrieved 2023-11-04. 
  4. ↑ 4.0 4.1 Sloane, N. J. A., ed. "Sequence A003601 (Numbers n such that the average of the divisors of n is an integer)". OEIS Foundation. https://oeis.org/A003601. 
  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.)". OEIS Foundation. https://oeis.org/A001065. 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).)". OEIS Foundation. https://oeis.org/A016105. 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. 
  8. ↑ Sloane, N. J. A., ed. "Sequence A164843 (The smallest magic constant of an n X n magic square with distinct prime entries.)". OEIS Foundation. https://oeis.org/A164843. 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.)". OEIS Foundation. https://oeis.org/A000396. Retrieved 2023-11-04. 
  10. ↑ Sloane, N. J. A., ed. "Sequence A000040 (The prime numbers.)". OEIS Foundation. https://oeis.org/A000040. Retrieved 2023-11-04. 
  11. ↑ Sloane, N. J. A., ed. "Sequence A006450 (Prime-indexed primes: primes with prime subscripts.)". OEIS Foundation. https://oeis.org/A006450. Retrieved 2023-11-04. 
  12. ↑ Sloane, N. J. A., ed. "Sequence A249911 (60–gonal number)". OEIS Foundation. https://oeis.org/A249911. 
  13. ↑ Sloane, N. J. A., ed. "Sequence A002827 (Unitary perfect numbers: numbers k such that usigma(k) - k equals k.)". OEIS Foundation. https://oeis.org/A002827. Retrieved 2023-11-04. 
  14. ↑ Sloane, N. J. A., ed. "Sequence A001595 (Leonardo numbers)". OEIS Foundation. https://oeis.org/A001595. 
  15. ↑ Sloane, N. J. A., ed. "Sequence A001383 (Number of n-node rooted trees of height at most 3)". OEIS Foundation. https://oeis.org/A001383. 
  16. ↑ Sloane, N. J. A., ed. "Sequence A000664 (Number of graphs with n edges)". OEIS Foundation. https://oeis.org/A000664. 
  17. ↑ Sloane, N. J. A., ed. "Sequence A002816 (Number of polygons that can be formed from n points on a circle, no two adjacent)". OEIS Foundation. https://oeis.org/A002816. 
  18. ↑ "Pub quiz". Tes Magazine. February 9, 2007. https://www.tes.com/magazine/archive/pub-quiz-41. Retrieved 2022-06-27. 



Retrieved from "https://handwiki.org/wiki/index.php?title=177_(number)&oldid=3368774"