8503
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 16
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 9288
- Proper Divisor Sum (Aliquot Sum)
- 785
- 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
- 7720
- Möbius Function
- 1
- Radical
- 8503
- 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
- 83
- 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
- s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Lucas numbers), t = A014306.at n=32A024477
- Number of partitions of n into parts not of the form 25k, 25k+10 or 25k-10. Also number of partitions with at most 9 parts of size 1 and differences between parts at distance 11 are greater than 1.at n=32A036009
- Numbers whose base-5 representation contains exactly two 0's and three 3's.at n=23A045198
- Smallest value of x such that M(x) = n, where M() is Mertens's function A002321.at n=29A051400
- Inverse Mertens function: smallest k such that |M(k)| = n, where M(x) is Mertens's function A002321.at n=29A051402
- Number of lucky 2,6 triples <= 10^n.at n=7A055726
- An inverse to Mertens's function: smallest k >= 2 such that Mertens's function |M(k)| (see A002321) is equal to n.at n=30A060434
- Number of standard shifted tableaux with n entries.at n=12A061343
- Number of compositions of n such that two adjacent parts are not equal modulo 5.at n=18A062203
- a(1) = 1, a(n+1) is the sum of a(n) and ceiling( arithmetic mean of a(1) ... a(n) ).at n=32A065095
- Records in A117677.at n=39A117679
- Least semiprime s for which the Mertens function M(s) = n.at n=33A123173
- Expansion of Product_{k > 0} (1 + f(k)*x^k), where f(k) = A147952(A004001(k)).at n=34A147982
- a(n) = (p(n)*p(n+2) - 3*p(n+1))/2, where p(n) is the n-th odd prime.at n=29A152529
- Table T(n,3) read by rows with T(n,1)=a,T(n,2)=b,T(n,3)=c and ((a*M(n))^3)*((a*M(n))^3+b)+c is prime for the least a with least b and c = -1 or 1 and M(n) = n-th Mersenne prime.at n=69A158695
- Integers of the form 4n+3 for which Sum_{i=1..u} J(i,4n+3) obtains value zero exactly 3 times, when u ranges from 1 to (4n+3). Here J(i,k) is the Jacobi symbol.at n=31A166053
- Numbers with distinct digits appearing in partition of decimal expansion of square root of 2. (A002193).at n=23A167834
- Augmentation of the Euler triangle A008292. See Comments.at n=23A193590
- Conjectured number of digits in highest power of n with no four consecutive identical digits.at n=5A216142
- Consider a k-digit number m = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + ... + d_(2)*10 + d_(1). Sequence lists the numbers m that divide Sum_{i=1..k-1}{d_(i)^d_(i+1)}+d_(k)^d_(1).at n=15A243024