101
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 2
- Digital Root
- 2
- Palindromic Number
- yes
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 102
- 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
- 100
- Möbius Function
- -1
- Radical
- 101
- 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
- 25
- Smith Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- yes
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 26
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- einshunderteins· ordinal: einshunderteinsste
- English
- one hundred one· ordinal: one hundred first
- Spanish
- ciento uno· ordinal: 101º
- French
- cent un· ordinal: cent unième
- Italian
- centouno· ordinal: 101º
- Latin
- centum unus· ordinal: 101.
- Portuguese
- cento e um· ordinal: 101º
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=46A000028
- a(n) is the number of partitions of n (the partition numbers).at n=13A000041
- Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).at n=41A000115
- Kendall-Mann numbers: the most common number of inversions in a permutation on n letters is floor(n*(n-1)/4); a(n) is the number of permutations with this many inversions.at n=5A000140
- Lower Wythoff sequence (a Beatty sequence): a(n) = floor(n*phi), where phi = (1+sqrt(5))/2 = A001622.at n=62A000201
- A Beatty sequence: floor(n*(e-1)).at n=58A000210
- 3*n - 2*floor(sqrt(4*n+5)) + 5.at n=40A000277
- Numbers m such that Fibonacci(m) ends with m.at n=11A000350
- 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=13A000375
- 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=13A000376
- Numbers that are the sum of 2 nonzero squares.at n=35A000404
- Numbers that are the sum of three nonzero squares.at n=66A000408
- Numbers that are the sum of 2 but no fewer nonzero squares.at n=33A000415
- Primes and squares of primes.at n=29A000430
- n written in base where place values are positive cubes.at n=28A000433
- The greedy sequence of integers which avoids 3-term geometric progressions.at n=72A000452
- Numbers written in base of triangular numbers.at n=6A000462
- a(0)=1; a(n) = 10^n + 1, n >= 1.at n=2A000533
- Number of stereoisomeric paraffins with n carbon atoms.at n=9A000626
- n-th superior highly composite number A002201(n) is product of first n terms of this sequence.at n=42A000705