177 (number)

For other topics, see 177 (disambiguation).

← 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

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

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]

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. 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. 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.