157
domain: N
Properties
Digital Properties
- Digit Count
- 3
- Digit Sum
- 13
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 158
- 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
- 156
- Möbius Function
- -1
- Radical
- 157
- 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
- 36
- 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
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 37
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Names
- German
- einshundertsiebenundfünfzig· ordinal: einshundertsiebenundfünfzigste
- English
- one hundred fifty-seven· ordinal: one hundred fifty-seventh
- Spanish
- ciento cincuenta y siete· ordinal: 157º
- French
- cent cinquante-sept· ordinal: cent cinquante-septième
- Italian
- centocinquantasette· ordinal: 157º
- Latin
- centum quinquaginta septem· ordinal: 157.
- Portuguese
- cento e cinquenta e sete· ordinal: 157º
Appears in sequences
- Local stops on New York City 1 Train (Broadway-7 Avenue Local) subway.at n=19A000053
- Number of odd integers <= 2^n of form x^2 + y^2.at n=9A000074
- Denumerants: Expansion of 1/((1-x)*(1-x^2)*(1-x^5)).at n=52A000115
- 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=12A000223
- a(0) = 1, a(1) = 4, and a(n) = a(n-1) + a(n-2) for n >= 2.at n=9A000285
- Numbers that are the sum of 2 nonzero squares.at n=53A000404
- Numbers that are the sum of 2 but no fewer nonzero squares.at n=51A000415
- Primes and squares of primes.at n=41A000430
- Number of nonnegative solutions to x^2 + y^2 + z^2 <= n.at n=35A000606
- Number of partitions of n into prime parts.at n=34A000607
- Landau's approximation to population of x^2 + y^2 <= 2^n.at n=9A000690
- Numbers k such that (1,k) is "good".at n=9A000696
- Expansion of Product_{k>=0} (1 + x^(2k+1)); number of partitions of n into distinct odd parts; number of self-conjugate partitions; number of symmetric Ferrers graphs with n nodes.at n=56A000700
- n-th superior highly composite number A002201(n) is product of first n terms of this sequence.at n=59A000705
- Boustrophedon transform of sequence 1,1,0,0,0,0,...at n=6A000756
- Primes p of the form 3k+1 such that -sqrt(p) < sum_{x=1..p} cos(2*Pi*x^3/p) < sqrt(p).at n=5A000922
- Irregular primes: primes p such that at least one of the numerators of the Bernoulli numbers B_2, B_4, ..., B_{p-3} (A000367) is divisible by p.at n=7A000928
- Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).at n=50A000961
- a(n) = least m such that if a/b < c/d where a,b,c,d are integers in [0,n], then a/b < k/m < c/d for some integer k.at n=15A001000
- a(n+1) = n*a(n) + a(n-1) with a(0)=1, a(1)=0.at n=6A001053