12306
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 12
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 16
- Divisor Sum
- 28224
- Proper Divisor Sum (Aliquot Sum)
- 15918
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 3504
- Möbius Function
- 1
- Radical
- 12306
- Omega Function (Ω)
- 4
- 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
- 94
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- no
- Composite Number
- yes
- Semiprime
- no
- 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
- G.f.: Product_{k>=1} (1 + x^(2*k - 1)) / (1 - x^(2*k)).at n=46A006950
- a(n) is the sum over all floor(k^3/n), k=0 to n inclusive.at n=35A014818
- Expansion of Product_{m>=1} (1+x^m)^3.at n=19A022568
- Convolution of composite numbers and odd numbers.at n=26A023650
- Number of partitions of n into parts not of the form 13k, 13k+5 or 13k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 5 are greater than 1.at n=38A035953
- Number of conjugacy classes in the symmetric group S_n that have even number of elements.at n=33A060643
- Numbers k such that usigma(k) is a square and sets a new record for such squares.at n=19A064443
- G.f.: Product_{k>0} (1-x^(2k-1))/(1-x^(2k)).at n=46A106507
- Number of partitions of n which represent first player winning Chomp positions with multiple winning moves.at n=37A112473
- Number of partitions of n-1 boys and one girl with no couple.at n=27A120452
- Square array, read by antidiagonals, where row n+1 equals the partial sums of the sequence resulting from removing the terms in the first column and main diagonal from row n, for n>=0, with row 0 consisting of all 1's.at n=45A130462
- Square array, read by antidiagonals, where row n+1 equals the partial sums of the sequence resulting from removing the terms in the first column and main diagonal from row n, for n>=0, with row 0 consisting of all 1's.at n=46A130462
- First column of square array A130462.at n=9A130463
- Number of compositions of n such that the largest part is coprime to every other part.at n=16A130709
- Number of partitions of n minus number of divisors of n.at n=33A144300
- Triangle T(n,k) read by rows: T(n, k) = (m*n - m*k + 1)*T(n - 1, k - 1) + (9*k - 8)*(m*k - (m - 1))*T(n - 1, k) where m = 0.at n=33A166979
- Number of 2Xn 0..1 arrays with exactly floor(2Xn/2) elements unequal to at least one horizontal, diagonal or antidiagonal neighbor, with new values introduced in row major 0..1 order.at n=12A222510
- Number of (n+3) X 4 0..2 matrices with each 4 X 4 subblock idempotent.at n=7A224721
- T(n,k)=Number of (n+3)X(k+3) 0..2 matrices with each 4X4 subblock idempotent.at n=28A224728
- T(n,k)=Number of (n+3)X(k+3) 0..2 matrices with each 4X4 subblock idempotent.at n=35A224728