10528
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 16
- Digital Root
- 7
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 24
- Divisor Sum
- 24192
- Proper Divisor Sum (Aliquot Sum)
- 13664
- Abundant Number
- yes
- Perfect Number
- no
- Deficient Number
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 4416
- Möbius Function
- 0
- Radical
- 658
- Omega Function (Ω)
- 7
- Little Omega Function (ω)
- 3
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
- yes
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 55
- 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
- Numbers k such that sigma(k) = sigma(k+12).at n=37A015882
- Number of different bracelets with 6 beads of at most n colors, allowing turning over.at n=7A027670
- Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 51.at n=29A031549
- 5-digit terms in the continued fraction for Pi.at n=8A048960
- Numbers k such that phi(x) = k has exactly 12 solutions.at n=32A060675
- Maximal term in Collatz-iteration started at 3^n+1.at n=8A087972
- Maximal term in Collatz-iteration started at 3^n.at n=6A087973
- Numbers k for which 16*k+1, 16*k+3 and 16*k+15 are primes.at n=42A123997
- Expansion of ((b(q)*c(q))^3 - 8*(b(q^2)*c(q^2))^3) / 27 in powers of q where b(), c() are cubic AGM theta functions.at n=31A128486
- Coefficients of the v=1 member of a family of certain orthogonal polynomials.at n=33A129065
- Denominators of the Engel partial sums for L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.at n=5A129661
- a(n) = 2*a(n-1) + 16*a(n-2) + 16*a(n-3) for n>3 with a(1)=1, a(2)=14, a(3)=60.at n=5A140184
- The LerchPhi functional part of A060187 MacMahon numbers is treated/ solved for as a curvature to give a set of polynomial triangle sequence coefficients: p(x,n) = Sum[A060187(n,m)*x^(m-1),{m,0,n}]; q(x,n)=k from Solve[FullSimplify[ExpandAll[p[x, n]/(x - 1)^n]] - (1 + k/x^2) == 0, k].at n=17A146543
- The LerchPhi functional part of A060187 MacMahon numbers is treated/ solved for as a curvature to give a set of polynomial triangle sequence coefficients: p(x,n) = Sum[A060187(n,m)*x^(m-1),{m,0,n}]; q(x,n)=k from Solve[FullSimplify[ExpandAll[p[x, n]/(x - 1)^n]] - (1 + k/x^2) == 0, k].at n=19A146543
- Coefficients of Pascal's triangle polynomial minus MacMahon polynomial A060187 with a power of x divided out: q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x.at n=11A146568
- Coefficients of Pascal's triangle polynomial minus MacMahon polynomial A060187 with a power of x divided out: q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((x+1)^n-q(x,n))/x.at n=13A146568
- Coefficients of Pascal's triangle polynomial minus MacMahon polynomial A060187 with minus the first and last row terms and powers of x divided out: f(n)=3^n - 2*n - 1; q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x.at n=3A146745
- Coefficients of Pascal's triangle polynomial minus MacMahon polynomial A060187 with minus the first and last row terms and powers of x divided out: f(n)=3^n - 2*n - 1; q(x,n)=2^n*(1 - x)^(n + 1)* LerchPhi[x, -n, 1/2]; p(x,n)=((q[x, n] - (x + 1)^n)/x - f[n] - f[n]*x^(n - 2))/x.at n=5A146745
- 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, 0), (-1, 0, 0), (1, 0, 1), (1, 1, -1), (1, 1, 0)}.at n=7A150748
- Triangle read by rows: T(n,k) = A129178(n,k) * (n*(n-1)/2 - k).at n=32A159323