9921
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 21
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 13232
- Proper Divisor Sum (Aliquot Sum)
- 3311
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 6612
- Möbius Function
- 1
- Radical
- 9921
- Omega Function (Ω)
- 2
- Little Omega Function (ω)
- 2
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- no
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- no
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 135
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- yes
- Squarefree Number
- yes
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Number of certain self-avoiding walks with n steps on square lattice (see reference for precise definition).at n=15A002976
- f-vectors for simplicial complexes of dimension at most 1 (graphs) on at most n-1 vertices.at n=39A011826
- Position of n^3 + 9 in A024975.at n=44A024979
- Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 66.at n=29A031564
- Numbers k such that the period of the continued fraction for sqrt(k) contains exactly 58 ones.at n=14A031826
- Exactly 5 digits from {1,2,3,4,5,6,7,8,9} can precede a(n) to form a lucky number.at n=34A032701
- Partial sums of sequence (essentially A002378): 1, 2, 6, 12, 20, 30, 42, 56, 72, 90, ...at n=30A064999
- Numbers k for which 10*2^k + 3 is a prime (giving terms of A068712).at n=47A068713
- Treated as strings, n begins with Floor(sqrt(n)).at n=44A069086
- Centered 20-gonal (or icosagonal) numbers.at n=31A069133
- Berend Jan van der Zwaag's conjectured complete list of numbers that start different "expanding periodic loops" under the mapping described in A053392 and A060630.at n=3A103117
- a(1) = 1; for n>1, a(n) = the smallest number p > a(n-1) such that (a(n-1)+p)/2 is a cube.at n=20A126950
- Numbers k such that the numerator of the Bernoulli number B(2k) ends with the digits 691.at n=39A132184
- a(n) = 242*n - 1.at n=40A157961
- a(n) = (4*n^3 - 6*n^2 + 8*n + 3)/3.at n=20A161712
- a(n) = b(n) + b(n+1) + 2, where b() = A000930().at n=23A170934
- 11^n mod 10000.at n=31A216132
- a(n) = sum_{k=0}^n binomial(n,k)^2*4^k*A000108(k).at n=4A228511
- a(n) = 6*n^2 + 8*n + 1.at n=40A239325
- Expansion of -(sqrt(x^4-4*x^3-6*x^2-4*x+1) +x^2-2*x-1)/4.at n=9A247195