10505
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
- 8
- Divisor Sum
- 13824
- Proper Divisor Sum (Aliquot Sum)
- 3319
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 7600
- Möbius Function
- -1
- Radical
- 10505
- Omega Function (Ω)
- 3
- 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
- no
- Harshad Number
- yes
- Narcissistic Number
- no
- Collatz Steps
- 148
- 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
- no
- Odd
- yes
Appears in sequences
- sec(cos(x)*sin(x))=1+1/2!*x^2-11/4!*x^4-83/6!*x^6+10505/8!*x^8...at n=4A012478
- a(n) = Fibonacci(n) - n^2.at n=21A014283
- a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n+1-k), where k = [ (n+1)/2 ], s = A000201 (lower Wythoff sequence).at n=35A024685
- a(n) = s(1)s(n) + s(2)s(n-1) + ... + s(k)s(n-k+1), where k = [ n/2 ], s = A000201 (lower Wythoff sequence).at n=34A025118
- Numbers in which 0,1,2,3,4,5 all occur in base 6.at n=24A031947
- "DFK" (bracelet, size, unlabeled) transform of 1,2,3,4...at n=17A032216
- Multiplicity of highest weight (or singular) vectors associated with character chi_36 of Monster module.at n=38A034424
- Number of ternary rooted trees with n nodes and height exactly 8.at n=15A036423
- Smallest k>1 such that k(p-1)-1 is divisible by p^2, p=n-th prime.at n=26A039914
- Numbers of the form p*q*r where p,q,r are distinct odd palindromic primes (odd terms from A002385).at n=39A046405
- Digitally balanced numbers in base 6: equal numbers of 0's, 1's, ..., 5's.at n=24A049357
- Numbers k such that 171*2^k-1 is prime.at n=30A050837
- a(n) = (2*n - 1)*(7*n^2 - 7*n + 6)/6.at n=16A063490
- Numbers n such that A065863(n) = 1, i.e., prime(n) mod (n - Pi(n)) = 1.at n=23A072623
- Multiples of 11 with digit sum 11, with no zero digits in odd places.at n=12A083512
- a(n) = (1/6)*Sum_{k=0..n} binomial(n,k)*Fibonacci(k)*6^k.at n=4A087579
- Pell equation solutions (5*a(n))^2 - 26*b(n)^2 = -1 with b(n):=A097727(n), n >= 0.at n=2A097726
- Number of permutations of length n which avoid the patterns 1423, 2134, 3214.at n=8A116764
- Numbers of the form k^2 - k - 1 whose digit sum is also a number of the form k^2 - k - 1.at n=38A117746
- p^2-p-1 that is not prime, where p is prime.at n=13A119609