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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 ninth Leyland number, where^[1]

$177=2^{7}+7^{2}.$

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 $M$ of the smallest full $3\times 3$ magic square consisting of distinct primes is 177:^[7]^[8]^[b]

47	89	101
113	59	5
17	29	71

Where the central cell ${\text{ }}59={\tfrac {177}{3}}{\text{ }}$ represents the seventeenth prime number,^[10] and seventh super-prime;^[11] equal to the sum of all prime numbers up to 17, including one: $1+2+3+5+7+11+13+17=59.$

177 is also an arithmetic number, whose $\sigma _{0}$ holds an integer arithmetic mean of $60$ — it is the one hundred and nineteenth indexed member in this sequence,^[4] where ${\text{ }}59+60=119.$ 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]

In other fields

177 is the second highest score for a flight of three darts, below the highest score of 180.^[18]

Notes

^ 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 $n = p \times q$ 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

^ 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.

[7] 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 $n = p \times q$ 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]

[11] 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.

[16] Where 60 is the value of the second unitary perfect number, after 6.^[13]

[1] Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[2] 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.

[DiscSemip-3] 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.

[ArithNum-4] 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.

[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.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 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).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.

[8] 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.

[PrimeMS-9] 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.

[10] 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.

[12] Sloane, N. J. A. (ed.). "Sequence A000040 (The prime numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-11-04.

[13] 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.

[14] Sloane, N. J. A. (ed.). "Sequence A249911 (60–gonal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[15] 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.

[17] Sloane, N. J. A. (ed.). "Sequence A001595 (Leonardo numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[18] 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.

[19] Sloane, N. J. A. (ed.). "Sequence A000664 (Number of graphs with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

[20] 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.

[21] "Pub quiz". Tes Magazine. February 9, 2007. Retrieved 2022-06-27.

[1]

[2]

[3]

[a]

[7]

[8]

[b]

[10]

[11]

[4]

[12]

[c]

[14]

[15]

[16]

[17]

[18]

[5]

[6]

[9]

[13]

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177 (number)

In mathematics

In other fields

See also

Notes

References

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