13378
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 22
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 20070
- Proper Divisor Sum (Aliquot Sum)
- 6692
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 6688
- Möbius Function
- 1
- Radical
- 13378
- 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
- no
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 45
- 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
- yes
- Odd
- no
Appears in sequences
- Numbers that are the sum of 8 positive 7th powers.at n=41A003375
- Numbers that are the sum of 3 nonzero 8th powers.at n=8A003381
- Numbers that are the sum of at most 3 nonzero 8th powers.at n=18A004876
- Numbers that are the sum of at most 4 nonzero 8th powers.at n=28A004877
- Numbers k such that phi(sigma(k)+k) = sigma(k-phi(k)), where phi is A000010 and sigma is A000203.at n=29A063710
- G.f.: A(x) = Product_{n>=0} 1/(1 - a(n)*x^(n+1)) = Sum_{n>=0} a(n)*x^n.at n=12A093637
- a(n) is the smallest number whose English name has the letter "t" in the n-th position, or -1 if no such number exists.at n=39A164792
- a(n) is the smallest number whose English name has the letter "h" in the n-th position, or -1 if no such number exists.at n=38A164795
- Triangle read by rows: T(n,k) is the number of peakless Motzkin paths of length n having k UHD's; here U=(1,1), H=(1,0), and D=(1,-1).at n=46A190172
- G.f. satisfies: A(x) = exp( Sum_{n>=} (x^n/n)*[Sum_{d|n} d*A(x)^d]^n ).at n=5A192769
- Second elementary symmetric function of the first n terms of (1,2,2,3,3,4,4,5,5...).at n=22A203298
- Expansion of F(x) where F(x) = 1 + x / (1 - x * F(x) * F(+x^2) ).at n=12A238427
- Expansion of -x*d(log((1-x*(2/sqrt(3*x)) * sin((1/3) * arcsin(sqrt(27*x/4))))))/dx.at n=7A242798
- Number of nX(n+3) arrays of permutations of n+3 copies of 0..n-1 with every element equal to or 1 greater than any north, southwest or northwest neighbors modulo n and the upper left element equal to 0.at n=7A267199
- a(1)=1. Thereafter, a(n+1) is the greatest divisor of s(n) which is prime to a(n), where s(n) is the n-th partial sum.at n=62A351743
- Square array T(n,k), n >= 1, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=1..n} (j * floor(n/j))^k.at n=57A356250
- Triangle read by rows: the almost-Riordan array ( 1/(1-x) | 2/((1-x)*(1+sqrt(1-4*x))), (1-2*x-sqrt(1-4*x))/(2*x) ).at n=59A373744
- Array read by downward antidiagonals: A(n,k) = Sum_{i=0..n-1} Sum_{j=0..k+1} binomial(n-1,i)*binomial(k+1,j)*A(i,j) with A(0,k) = 1, n >= 0, k >= 0.at n=47A383410