113
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 5
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 114
- 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
- 112
- Möbius Function
- -1
- Radical
- 113
- 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
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 12
- Smith Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- yes
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 30
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- einshundertdreizehn· ordinal: einshundertdreizehnste
- English
- one hundred thirteen· ordinal: one hundred thirteenth
- Spanish
- ciento trece· ordinal: 113º
- French
- cent treize· ordinal: cent treizième
- Italian
- centotredici· ordinal: 113º
- Latin
- centum tredecim· ordinal: 113.
- Portuguese
- cento e treze· ordinal: 113º
Appears in sequences
- 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=55A000028
- A Beatty sequence: floor(n*(e-1)).at n=65A000210
- a(0)=2; for n>=1, a(n) = smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists.at n=7A000230
- Number of points of norm <= n^2 in square lattice.at n=6A000328
- 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=14A000375
- Numbers that are the sum of 2 nonzero squares.at n=39A000404
- Numbers that are the sum of 2 but no fewer nonzero squares.at n=37A000415
- Primes and squares of primes.at n=33A000430
- n written in base where place values are positive cubes.at n=38A000433
- Number of nonnegative solutions of x^2 + y^2 = z in first n shells.at n=54A000592
- One half of number of non-self-conjugate partitions; also half of number of asymmetric Ferrers graphs with n nodes.at n=16A000701
- n-th superior highly composite number A002201(n) is product of first n terms of this sequence.at n=47A000705
- Numbers beginning with a vowel in English.at n=27A000852
- Numbers beginning with letter 'o' in English.at n=14A000865
- a(2n) = n+2, a(2n-1) = smallest number requiring n+2 letters in English.at n=36A000916
- Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).at n=40A000961
- a(n) = ceiling(n^2/2).at n=15A000982
- Length of one version of Kolakoski sequence {A000002(i)} at n-th growth stage.at n=12A001083
- Maximal number of pairwise relatively prime polynomials of degree n over GF(2).at n=10A001115
- Primes with 3 as smallest primitive root.at n=6A001123