10307
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 11
- Digital Root
- 2
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 4
- Divisor Sum
- 11256
- Proper Divisor Sum (Aliquot Sum)
- 949
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 9360
- Möbius Function
- 1
- Radical
- 10307
- 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
- yes
- Narcissistic Number
- no
- Collatz Steps
- 148
- 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
- Convolution of natural numbers with Beatty sequence for the golden mean A000201.at n=32A023541
- a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2), t = A000045 (Fibonacci numbers).at n=16A023860
- Number of partitions of n into parts not of form 4k+2, 24k, 24k+9 or 24k-9. Also number of partitions in which no odd part is repeated, with at most 4 parts of size less than or equal to 2 and where differences between parts at distance 5 are greater than 1 when the smallest part is odd and greater than 2 when the smallest part is even.at n=48A036033
- Numbers k such that k^2 + k + 1, k^3 + k + 1 and k^4 + k + 1 are all prime.at n=33A057683
- Number of function calls required to compute ack(3,n), where ack denotes the Ackermann function.at n=4A074877
- Multiples of 11 with digit sum 11, with no zero digits in odd places.at n=10A083512
- Numbers k such that (k / sum of digits of k) and (k+1 / sum of digits of k+1) are both prime.at n=14A085775
- Numerator of sqrt(2) * Integral_{x=0..sqrt(1/3)} 1/(1-x^2)^(n+3/2) dx.at n=4A089342
- Interpolate 0's between each pair of digits of n-th prime.at n=32A092909
- k such that k-th prime is of the form 2n^2 + 3n + 3.at n=35A096690
- Triangle T(n,k) read by rows: number of lattice paths from (0,0) to (0,2n) with steps (1,1) or (1,-1) that stay between the lines y=0 and y=k.at n=38A101475
- Numbers n such that the numerator of Sum_{i=1..n} (1/i^2), in reduced form, is prime.at n=23A111354
- Number of distinct Tsuro tiles which are n-gonal in shape and have 2 points per side.at n=7A132105
- Beginning of a run of 4 consecutive Niven (or Harshad) numbers.at n=11A141769
- Numbers k such that k, k + 1 and k + 2 are 3 consecutive Harshad numbers.at n=27A154701
- Row sums of generalized Lucas-Pascal triangle: A164855.at n=4A164856
- a(n) = Floor(Fibonacci(n)^(1/Pi)).at n=62A171962
- Principal diagonal of the convolution array A213576.at n=8A213577
- Number of ways to write highly composite numbers (A002182(n)) as the difference of two primes, both <= 2*A002182(n).at n=33A228945
- a(1)=2; thereafter, a(n) is the smallest number not occurring earlier such that Kronecker(a(k), a(n)) = -1 for the next n indices k = n+1, n+2, ..., 2n.at n=17A249692