From Wikipedia, the free encyclopedia
Natural number
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]
177
=
2
7
+
7
2
.
{\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
M
{\displaystyle M}
of the smallest full
3
×
3
{\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
59
=
177
3
{\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:
1
+
2
+
3
+
5
+
7
+
11
+
13
+
17
=
59.
{\displaystyle 1+2+3+5+7+11+13+17=59.}
177 is also an
arithmetic number , whose
σ
0
{\displaystyle \sigma _{0}}
holds an integer
arithmetic mean of
60
{\displaystyle 60}
— it is the one hundred and nineteenth
indexed member in this sequence,
[4] where
59
+
60
=
119.
{\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]
See also
The year
AD 177 or
177 BC
Notes
References
^
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 .
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000