177 (number)

Last updated
← 176 177 178 →
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
Binary 101100012
Ternary 201203
Senary 4536
Octal 2618
Duodecimal 12912
Hexadecimal B116

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

Contents

In mathematics

One hundred and seventy-seven is the ninth Leyland number, where [1]

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 of the smallest full magic square consisting of distinct primes is 177: [7] [8] [b]

4789101
113595
172971

Where the central cell represents the seventeenth prime number, [10] and seventh super-prime; [11] equal to the sum of all prime numbers up to 17 , including one:

177 is also an arithmetic number, whose holds an integer arithmetic mean of — it is the one hundred and nineteenth indexed member in this sequence, [4] where 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]

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]

Related Research Articles

15 (fifteen) is the natural number following 14 and preceding 16.

21 (twenty-one) is the natural number following 20 and preceding 22.

33 (thirty-three) is the natural number following 32 and preceding 34.

70 (seventy) is the natural number following 69 and preceding 71.

90 (ninety) is the natural number following 89 and preceding 91.

29 (twenty-nine) is the natural number following 28 and preceding 30. It is a prime number.

72 (seventy-two) is the natural number following 71 and preceding 73. It is half a gross or six dozen.

35 (thirty-five) is the natural number following 34 and preceding 36

86 (eighty-six) is the natural number following 85 and preceding 87.

34 (thirty-four) is the natural number following 33 and preceding 35.

46 (forty-six) is the natural number following 45 and preceding 47.

58 (fifty-eight) is the natural number following 57 and preceding 59.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

216 is the natural number following 215 and preceding 217. It is a cube, and is often called Plato's number, although it is not certain that this is the number intended by Plato.

181 is the natural number following 180 and preceding 182.

1728 is the natural number following 1727 and preceding 1729. It is a dozen gross, or one great gross. It is also the number of cubic inches in a cubic foot.

240 is the natural number following 239 and preceding 241.

888 is the natural number following 887 and preceding 889.

262 is a natural number preceded by the number 261 and followed by 263. It has the prime factorization 2·131.

1105 is the natural number following 1104 and preceding 1106.

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA076980(Leyland numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA001358(Semiprimes (or biprimes): products of two primes.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-04.
  3. 1 2 Sloane, N. J. A. (ed.). "SequenceA006881(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. 1 2 Sloane, N. J. A. (ed.). "SequenceA003601(Numbers n such that the average of the divisors of n is an integer)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA001065(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.). "SequenceA016105(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.). "SequenceA164843(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.). "SequenceA000396(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.). "SequenceA000040(The prime numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2023-11-04.
  11. ↑ Sloane, N. J. A. (ed.). "SequenceA006450(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.). "SequenceA249911(60–gonal number)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  13. ↑ Sloane, N. J. A. (ed.). "SequenceA002827(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.). "SequenceA001595(Leonardo numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  15. ↑ Sloane, N. J. A. (ed.). "SequenceA001383(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.). "SequenceA000664(Number of graphs with n edges)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  17. ↑ Sloane, N. J. A. (ed.). "SequenceA002816(Number of polygons that can be formed from n points on a circle, no two adjacent)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  18. ↑ "Pub quiz". Tes Magazine. February 9, 2007. Retrieved 2022-06-27.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.