137
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 11
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 138
- 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
- 136
- Möbius Function
- -1
- Radical
- 137
- 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
- 90
- 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
- 33
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- einshundertsiebenunddreißig· ordinal: einshundertsiebenunddreißigste
- English
- one hundred thirty-seven· ordinal: one hundred thirty-seventh
- Spanish
- ciento treinta y siete· ordinal: 137º
- French
- cent trente-sept· ordinal: cent trente-septième
- Italian
- centotrentasette· ordinal: 137º
- Latin
- centum triginta septem· ordinal: 137.
- Portuguese
- cento e trinta e sete· ordinal: 137º
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=66A000028
- Local stops on New York City 1 Train (Broadway-7 Avenue Local) subway.at n=17A000053
- Number of positive integers <= 2^n of form x^2 + 4 y^2.at n=9A000072
- Central polygonal numbers (the Lazy Caterer's sequence): n(n+1)/2 + 1; or, maximal number of pieces formed when slicing a pancake with n cuts.at n=16A000124
- Positive zeros of Bessel function of order 0 rounded to nearest integer.at n=43A000134
- Let A(n) = #{(i,j): i^2 + j^2 <= n}, V(n) = Pi*n, P(n) = A(n) - V(n); A000099 gives values of n where |P(n)| sets a new record; sequence gives A(A000099(n)).at n=7A000323
- Numbers that are the sum of 2 nonzero squares.at n=47A000404
- Numbers that are the sum of 2 but no fewer nonzero squares.at n=45A000415
- Primes and squares of primes.at n=37A000430
- Number of permutations of [n] in which the longest increasing run has length 6.at n=7A000467
- Number of steps to reach 1 in sequence A000546.at n=10A000547
- A Beatty sequence: [ n(e+1) ].at n=36A000572
- Number of nonnegative solutions of x^2 + y^2 = z in first n shells.at n=64A000592
- n-th superior highly composite number A002201(n) is product of first n terms of this sequence.at n=51A000705
- Numbers that are not the sum of 4 tetrahedral numbers.at n=9A000797
- Genus of complete graph on n nodes.at n=43A000933
- Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).at n=46A000961
- a(n) = numerator of harmonic number H(n) = Sum_{i=1..n} 1/i.at n=4A001008
- Union of all numbers {p, q} where p and q are both primes or powers of primes and q = p+2.at n=33A001092
- Twin primes.at n=19A001097