177 (number)
| ||||
|---|---|---|---|---|
| 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.
In mathematics
[edit]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]
| 47 | 89 | 101 |
| 113 | 59 | 5 |
| 17 | 29 | 71 |
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
- 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
[edit]177 is the second highest score for a flight of three darts, below the highest score of 180.[18]
See also
[edit]Notes
[edit]- ^ 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] - ^ 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.
- ^ Where 60 is the value of the second unitary perfect number, after 6.[13]
References
[edit]- ^ Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A003601 (Numbers n such that the average of the divisors of n is an integer)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A249911 (60–gonal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A001595 (Leonardo numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ 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.
- ^ Sloane, N. J. A. (ed.). "Sequence A000664 (Number of graphs with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002816 (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.
- ^ "Pub quiz". Tes Magazine. February 9, 2007. Retrieved 2022-06-27.
