1337
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 14
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 1536
- Proper Divisor Sum (Aliquot Sum)
- 199
- 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
- 1140
- Möbius Function
- 1
- Radical
- 1337
- Omega Function (Ω)
- 2
- Little Omega Function (ω)
- 2
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
- 44
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- yes
- Squarefree Number
- yes
- Prime Power
- no
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Number of partitions into non-integral powers.at n=19A000148
- Number of partitions into non-integral powers.at n=5A000397
- Numbers k such that (k^2 + k + 1)/19 is prime.at n=36A002643
- a(n) = Sum_{k=0..n} C(n,k)*2^(k*(k+1)/2).at n=4A006898
- Coordination sequence T3 for Zeolite Code BOG.at n=26A008051
- Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^9)).at n=62A008674
- Coordination sequence T6 for Zeolite Code DFO.at n=28A009880
- sec(cos(x)*arcsin(x))=1+1/2!*x^2-3/4!*x^4-75/6!*x^6+1337/8!*x^8...at n=4A012491
- cos(sec(x)*arctan(x))=1-1/2!*x^2-3/4!*x^4-165/6!*x^6+1337/8!*x^8...at n=4A012806
- Expansion of e.g.f.: exp(sech(x)*arctanh(x))=1+x+1/2!*x^2-3/4!*x^4+20/5!*x^5+165/6!*x^6...at n=8A012882
- Convolution of primes with themselves.at n=10A014342
- Numbers k such that the continued fraction for sqrt(k) has period 18.at n=39A020357
- Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(5,20).at n=4A022021
- a(n) = a(n-1) + c(n+1) for n >= 3, a( ) increasing, given a(1)=1, a(2)=8; where c( ) is complement of a( ).at n=45A022954
- Positive numbers k such that k and 5*k are anagrams in base 8 (written in base 8).at n=2A023076
- Numbers k such that Fib(k) == 13 (mod k).at n=11A023178
- a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = A023532, t = A000201 (lower Wythoff sequence).at n=52A024373
- [ (4th elementary symmetric function of S(n))/(3rd elementary symmetric function of S(n)) ], where S(n) = {first n+3 positive integers congruent to 1 mod 4}.at n=50A024390
- a(n) = position of 2*n^3 in A003325.at n=43A024667
- a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n-k+1), where k = [ n/2 ], s = A023532, t = A000201 (lower Wythoff sequence).at n=51A025073