17380
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 19
- Digital Root
- 1
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 24
- Divisor Sum
- 40320
- Proper Divisor Sum (Aliquot Sum)
- 22940
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 6240
- Möbius Function
- 0
- Radical
- 8690
- Omega Function (Ω)
- 5
- Little Omega Function (ω)
- 4
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
- 53
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- Squarefree Number
- no
- 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
- Number of degree-n odd permutations of order 2.at n=11A001465
- Partial sums of fourth powers of Lucas numbers.at n=4A005972
- G.f.: 1/((1-x)*(1-x^2))^5.at n=11A038165
- Number of nonempty subsets of {1,2,...,n} in which exactly 2/5 of the elements are <= n/3.at n=17A047199
- Number of nonempty subsets of {1,2,...,n} in which exactly 2/5 of the elements are <= (n+1)/3.at n=17A048044
- Number of nonempty subsets of {1,2,...,n} in which exactly 2/5 of the elements are <= (n+2)/3.at n=17A048077
- Expansion of (5+10*x+x^2)/(1-x)^10.at n=5A059602
- E.g.f. cosh(x+x^2/2).at n=11A085386
- a(n) = 36*n^2 - 2*n.at n=21A158062
- a(n) = number of n-digit squares in base 10 such that there is at least one permutation that is also a square in base 10. Initial zeros are not allowed for any square.at n=8A177952
- G.f.: A(x) = INV(x-x^2 - x^2*INV(x-2*x^2 - x^2*INV(x-4*x^2 - x^2*INV(x-8*x^2 - x^2*INV(x-16*x^2 - ...))))), where INV(F(x)) = series reversion of F(x).at n=7A196711
- Total area of the shadows of the three views of a three-dimensional version of the shell model of partitions with n shells.at n=20A207380
- T(n,k)=Number of idempotent n X n -k..k matrices of rank n-1.at n=18A223450
- The number of overpartitions of n into parts congruent to 2, 4, or 5 modulo 6.at n=49A253136
- Numbers n such that the digital sum of n is the same as the digital sum of n^2 in both base 2 and base 10.at n=18A261640
- Triangle read by rows: T(n,m) (n >= m >= 1) = number of chambers (or regions) formed by drawing the line segments connecting any two of the (n+1) X (m+1) lattice points in an n X m lattice polygon.at n=24A288187
- a(1) = 24603, a(n) = n*a(n-1) but products that are not in A010784 are first reduced as in A320486 (see comments); continue until zero is reached.at n=44A321148
- Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of sqrt(2 / ( (1+2*(k-4)*x+((k+4)*x)^2) * (1-(k+4)*x+sqrt(1+2*(k-4)*x+((k+4)*x)^2)) )).at n=42A337464
- Expansion of sqrt(2 / ( (1-4*x+36*x^2) * (1-6*x+sqrt(1-4*x+36*x^2)) )).at n=6A337466