40,000 Explained

Number:	40000
Divisor:	35 total

40,000 (forty thousand) is the natural number that comes after 39,999 and before 40,001. It is the square of 200.

Selected numbers in the range 40001–49999

40001 to 40999

• 40320 = smallest factorial (8!) that is not a highly composite number
• 40425 = square pyramidal number
• 40585 = largest factorion^[1]
• 40678 = pentagonal pyramidal number
• 40755 = Triangular number, Pentagonal number, Hexagonal number, 390-gonal, 4077-gonal, and 13586-gonal number.
• 40804 = palindromic square

41000 to 41999

• 41041 = Carmichael number^[2]
• 41472 = 3-smooth number, number of reduced trees with 24 nodes
• 41586 = Large Schröder number
• 41616 = triangular square number^[3]
• 41835 = Motzkin number^[4]
• 41841 = 1/41841 = 0.0000239 is a repeating decimal with period 7

42000 to 42999

• 42680 = octahedral number^[5]
• 42875 = 35³
• 42925 = square pyramidal number

43000 to 43999

• 43261 = Markov number^[6]
• 43380 = number of nets of a dodecahedron
• 43390 = number of primes

\leq 2 ^{19} .^[7]

• 43560 = pentagonal pyramidal number
• 43691 = Wagstaff prime
• 43777 = smallest member of a prime sextuplet

44000 to 44999

• 44044 = palindrome of 79 after 6 iterations of the "reverse and add" iterative process^[8]
• 44100 = sum of the cubes of the first 20 positive integers 44,100 Hz is a common sampling frequency in digital audio (and is the standard for compact discs).
• 44444 = repdigit
• 44583 = number of partitions of 41
• 44721 = smallest positive integer such that the expression − ≤ 10⁻⁹
• 44724 = maximum number of days in which a human being has been verified to live (Jeanne Calment).^[9]
• 44944 = palindromic square

45000 to 45999

• 45360 = 26th highly composite number; smallest number with exactly 100 factors (including one and itself)

46000 to 46999

• 46080 = double factorial of 12
• 46233 = sum of the first eight factorials
• 46249 = 2nd number that can be written as

a ^{2+b!} in 3 ways

• 46368 = Fibonacci number
• 46656 = 216 = 36 = 6⁶, 3-smooth number
• 46657 = Carmichael number
• 46972 = number of prime knots with 14 crossings

47000 to 47999

• 47058 = primary pseudoperfect number
• 47160 = 10-th derivative of x^x at x=1^[10]
• 47321/33461 ≈ √2

48000 to 48999

• 48629 = number of trees with 17 unlabeled nodes
• 48734 = number of 22-bead necklaces (turning over is allowed) where complements are equivalent

49000 to 49999

• 49151 = Woodall number
• 49152 = 3-smooth number
• 49726 = pentagonal pyramidal number
• 49940 = number of 21-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed

Primes

There are 930 prime numbers between 40000 and 50000.

Notes and References

1. Web site: Sloane's A014080 : Factorions. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
2. Web site: Sloane's A002997 : Carmichael numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
3. Web site: Sloane's A001110 : Square triangular numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
4. Web site: Sloane's A001006 : Motzkin numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
5. Web site: Sloane's A005900 : Octahedral numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
6. Web site: Sloane's A002559 : Markoff (or Markov) numbers. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-06-15.
7. Number of primes <= 2^n.
8. Web site: Reversal-Addition Palindrome Test on 79.
9. Book: Amzallag . William . The Promise of Immortality . books/google.com . 22 September 2016 . Varegus Publishing . 978-2-9558558-1-2 . September 22, 2016.
10. n-th derivative of x^x at x=1. Also called Lehmer-Comtet numbers.