10705
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 13
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 12852
- Proper Divisor Sum (Aliquot Sum)
- 2147
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 8560
- Möbius Function
- 1
- Radical
- 10705
- 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
- 47
- Smith Number
- yes
- 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
- Expansion of e.g.f. arcsin(arcsin(x) * exp(x)).at n=7A012317
- Number of partitions satisfying (cn(0,5) = 0 and cn(1,5) = cn(4,5)).at n=53A036818
- Denominators of continued fraction convergents to sqrt(78).at n=8A041139
- Numerators of continued fraction convergents to sqrt(383).at n=6A041726
- Number of ways to write the numbers 1 through 3n on the faces of three n-sided dice, so that the 1st die beats the 2nd with probability > 1/2, the 2nd beats the 3rd with probability > 1/2 and the 3rd beats the 1st with probability > 1/2, and the first die contains the number 1.at n=5A121228
- a(n) = 104*n + 9977.at n=7A126978
- Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).at n=31A147593
- Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (1, -1, 0), (1, 1, 1)}.at n=8A149522
- Where records occur in A169784.at n=39A175437
- Numbers k that are the products of two distinct primes such that 2*k-1, 4*k-3, 8*k-7, 16*k-15 and 32*k-31 are also products of two distinct primes.at n=17A177214
- a(n) = floor((3*4^n + 2*3^n)/5).at n=7A178934
- The number of divisors d of n! such that the symmetric group on n letters contains no elements of order d.at n=16A211392
- Number of (w,x,y,z) with all terms in {1,...,n} and 2|w-x|=|x-y|+|y-z|.at n=25A212575
- Number of (n+1) X (1+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.at n=9A239530
- Number of partitions of n^2 into exactly 4 prime numbers.at n=27A243940
- Least positive integer k such that prime(prime(prime(k)))+ prime(prime(prime(k*n))) = 2*prime(prime(p)) for some prime p.at n=47A261583
- Solution of the complementary equation a(n) = 2*a(n-1) - b(n-2), where a(0) = 3, a(1) = 5, b(0) = 1, b(1) = 2, and (a(n)) and (b(n)) are increasing complementary sequences.at n=13A295060
- Expansion of Product_{k>0} (1 + Sum_{m>=0} x^(k*2^m)).at n=40A304393
- a(n) = n! * [x^n] exp(Sum_{k=1..n, gcd(n,k) = 1} x^k / k!).at n=12A335797
- Inverse Moebius transform of tetranacci number (A000078).at n=17A357239