31
domain: N
Properties
Digital Properties
- Digit Count
- 2
- Digit Sum
- 4
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 32
- Proper Divisor Sum (Aliquot Sum)
- 1
- 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
- 30
- Möbius Function
- -1
- Radical
- 31
- Omega Function (Ω)
- 1
- Little Omega Function (ω)
- 1
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
- 106
- Smith Number
- no
Classification
- Natural
- yes
- Even
- no
- Odd
- yes
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- yes
- Mersenne Prime
- yes
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 11
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Names
- German
- einunddreißig· ordinal: einunddreißigste
- English
- thirty-one· ordinal: thirty-first
- Spanish
- treinta y uno· ordinal: 31º
- French
- trente et un· ordinal: trente et unième
- Italian
- trentuno· ordinal: 31º
- Latin
- triginta unus· ordinal: 31.
- Portuguese
- trinta e um· ordinal: 31º
Appears in sequences
- Number of ways of making change for n cents using coins of 1, 2, 5, 10 cents.at n=18A000008
- Smallest prime power >= n.at n=29A000015
- Smallest prime power >= n.at n=30A000015
- Mosaic numbers or multiplicative projection of n: if n = Product (p_j^k_j) then a(n) = Product (p_j * k_j).at n=30A000026
- The positive integers. Also called the natural numbers, the whole numbers or the counting numbers, but these terms are ambiguous.at n=30A000027
- Let k = p_1^e_1 p_2^e_2 p_3^e_3 ... be the prime factorization of n. Sequence gives k such that the sum of the numbers of 1's in the binary expansions of e_1, e_2, e_3, ... is odd.at n=16A000028
- Numbers that are not squares (or, the nonsquares).at n=25A000037
- Mersenne exponents: primes p such that 2^p - 1 is prime. Then 2^p - 1 is called a Mersenne prime.at n=7A000043
- Partial sums of (unordered) ways of making change for n cents using coins of 1, 2, 5, 10 cents.at n=8A000064
- Odious numbers: numbers with an odd number of 1's in their binary expansion.at n=15A000069
- a(n) = floor(n^(3/2)).at n=10A000093
- Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).at n=21A000115
- Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes.at n=5A000127
- A nonlinear binomial sum.at n=5A000128
- Positive zeros of Bessel function of order 0 rounded to nearest integer.at n=9A000134
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=15A000203
- a(n) = sigma(n), the sum of the divisors of n. Also called sigma_1(n).at n=24A000203
- a(n) = a(n-1) + a(n-2) - 2, a(0) = 4, a(1) = 3.at n=7A000211
- Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1.at n=7A000213
- Number of squares mod n.at n=60A000224