13572
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 18
- Digital Root
- 9
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 36
- Divisor Sum
- 38220
- Proper Divisor Sum (Aliquot Sum)
- 24648
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 4032
- Möbius Function
- 0
- Radical
- 2262
- Omega Function (Ω)
- 6
- 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
- yes
Recreational
- Happy Number
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 45
- 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
- Expansion of (1+x^3*C^3)*C^3, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.at n=8A071736
- a(n) = Sum_{k=1..n} antisigma(k), where antisigma(i) = sum of the nondivisors of i that are between 1 and i.at n=43A076664
- Shuffle number in Guy's shuffle (see A035485) for the card that is at the top of the deck after n shuffles to come to the top again.at n=52A081059
- Number of 3 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.at n=17A086113
- Binomial transform of A033312.at n=7A097204
- a(n) = a(n-3) + A001654(n-1) with a(0)=0, a(1)=0 and a(2)=1.at n=12A115730
- First differences of A006128.at n=30A138137
- Integral quotients of products of consecutive composites divided by their sums: sums (divisors).at n=29A141091
- 6 times pentagonal numbers: a(n) = 3*n*(3*n-1).at n=39A152743
- G.f.: Product_{n>0} ((1+x^n)/(1-x^n))^n.at n=12A156616
- Partial sums of partial sums of (A001840 interleaved with zeros).at n=47A165189
- Triangle read by rows: T(n,0) = (n+1)^2, T(n,k) = T(n,k-1) + T(n-1,k) for 0 < k < n, and T(n,n) = T(n,n-1).at n=42A165996
- Numbers k such that there is 1 prime between 100*k and 100*k + 99.at n=7A186393
- Number of squares between powers of 2, floor(sqrt(2^(n+1))) - floor(sqrt(2^n)).at n=31A190568
- Integers that do not have a partition into a sum of an odd square and two (not necessarily distinct) triangular numbers.at n=31A191764
- T(n,k) gives the number of permutations of the set [n] that contain k occurrences of the subword (132); irregular array read by rows (n >= 0 and 0 <= k <= max(0, floor((n-1)/2))).at n=24A197365
- Number of 7 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.at n=10A208088
- a(3)=5, a(4)=8, a(5)=12; thereafter a(n) = a(n-1) + A000931(n+7).at n=25A220885
- Oblong numbers (A002378) whose sum of divisors is also an oblong number.at n=7A226363
- a(n) = 8*n^2 + 3*n + 1.at n=41A236267