51
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 6
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 72
- Proper Divisor Sum (Aliquot Sum)
- 21
- 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
- 32
- Möbius Function
- 1
- Radical
- 51
- Omega Function (Ω)
- 2
- Little Omega Function (ω)
- 2
Special
- Factorial
- no
- Catalan Number
- no
- Bell Number
- no
- Motzkin Number
- yes
- Primorial
- no
Figurate Numbers
- Fibonacci Number
- no
- Triangular Number
- no
- Perfect Square
- no
- Perfect Cube
- no
- Pentagonal Number
- yes
- Hexagonal Number
- no
- Lucas Number
- no
- Tetrahedral Number
- no
- Pell Number
- no
- Tribonacci Number
- no
- Pronic Number
- no
Recreational
- Happy Number
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 24
- Smith Number
- no
Classification
- Natural
- yes
- Even
- no
- Odd
- yes
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
Names
- German
- einundfünfzig· ordinal: einundfünfzigste
- English
- fifty-one· ordinal: fifty-first
- Spanish
- cincuenta y uno· ordinal: 51º
- French
- cinquante et un· ordinal: cinquante et unième
- Italian
- cinquantuno· ordinal: 51º
- Latin
- quinquaginta unus· ordinal: 51.
- Portuguese
- cinquenta e um· ordinal: 51º
Appears in sequences
- Number of groups of order n.at n=32A000001
- Coefficients of the 3rd-order mock theta function f(q).at n=23A000025
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=50A000026
- The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.at n=50A000027
- Numbers that are not squares (or, the nonsquares).at n=43A000037
- Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged.at n=10A000048
- 1-digit numbers arranged in alphabetical order, then the 2-digit numbers arranged in alphabetical order, then the 3-digit numbers, etc.at n=28A000052
- A Beatty sequence: a(n) = floor(n/(e-2)).at n=36A000062
- Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).at n=28A000115
- Coefficient of q^(2n-1) in the series expansion of Ramanujan's mock theta function f(q).at n=11A000199
- Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.at n=31A000201
- a(8i+j) = 13i + a(j), where 1<=j<=8.at n=31A000202
- A Beatty sequence: floor(n*(e-1)).at n=29A000210
- Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).at n=7A000223
- Remove all factors of 2 from n; or largest odd divisor of n; or odd part of n.at n=50A000265
- Pentagonal numbers: a(n) = n*(3*n-1)/2.at n=6A000326
- From a fractal set of positive Lebesgue measure, a self-replicating tiling with holes, the 4-reptile following the 2-reptile of Paul Levy.at n=34A000361
- Topswops (1): start by shuffling n cards labeled 1..n. If top card is m, reverse order of top m cards, then repeat. a(n) is the maximal number of steps before top card is 1.at n=10A000375
- Topswops (2): start by shuffling n cards labeled 1..n. If the top card is m, reverse the order of the top m cards. Repeat until 1 gets to the top, then stop. Suppose the whole deck is now sorted (if not, discard this case). a(n) is the maximal number of steps before 1 got to the top.at n=10A000376
- Sums of three squares: numbers of the form x^2 + y^2 + z^2.at n=44A000378