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177 (number)

FieldValue
number177
divisor1, 3, 59, 177

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

177 = 2^7 + 7^2.

The fifty-seventh semiprime is 177 (after the square of 13), and it is the 51st semiprime with distinct prime factors.

The magic constant M of the smallest full 3 \times 3 magic square consisting of distinct primes is 177:

172971

Where the central cell \text { } 59 = \tfrac {177}{3}\text { } represents the seventeenth prime number,{{Cite OEIS | A000040 |The prime numbers. |access-date=2023-11-04 }} and seventh super-prime; 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, where \text { }59 + 60 = 119. The first non-trivial 60-gonal number is 177.

177 is the tenth Leonardo number, part of a sequence of numbers closely related to the Fibonacci numbers.

In graph enumeration, there are

  • 177 rooted trees with 10 nodes and height at most 3,
  • 177 undirected graphs (not necessarily connected) that have 7 edges and no isolated vertices. 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.

Notes

References

References

  1. {{Cite OEIS. A076980. Leyland numbers
  2. {{Cite OEIS. A001358. Semiprimes (or biprimes): products of two primes.
  3. {{Cite OEIS. A006881. Squarefree semiprimes: Numbers that are the product of two distinct primes.
  4. {{Cite OEIS. A003601. Numbers n such that the average of the divisors of n is an integer
  5. {{Cite OEIS. A001065. Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.
  6. {{Cite OEIS. A016105. Blum integers: numbers of the form p * q where p and q are distinct primes congruent to 3 (mod 4).
  7. Madachy, Joseph S.. (1979). "Madachy's Mathematical Recreations". [[Dover Publications.
  8. {{Cite OEIS. A164843. The smallest magic constant of an n X n magic square with distinct prime entries.
  9. {{Cite OEIS. A000396. Perfect numbers k: k is equal to the sum of the proper divisors of k.
  10. {{Cite OEIS. A006450. Prime-indexed primes: primes with prime subscripts.
  11. {{cite OEIS. A249911. 60–gonal number
  12. {{Cite OEIS. A002827. Unitary perfect numbers: numbers k such that usigma(k) - k equals k.
  13. {{Cite OEIS. A001595. Leonardo numbers
  14. {{Cite OEIS. A001383. Number of n-node rooted trees of height at most 3
  15. {{Cite OEIS. A000664. Number of graphs with n edges
  16. {{Cite OEIS. A002816. Number of polygons that can be formed from n points on a circle, no two adjacent
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