6987
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 30
- Digital Root
- 3
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 9936
- Proper Divisor Sum (Aliquot Sum)
- 2949
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Highly Composite
- no
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 4352
- Möbius Function
- -1
- Radical
- 6987
- 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
- yes
- Harshad Number
- no
- Narcissistic Number
- no
- Collatz Steps
- 150
- 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
- Powers of sqrt(5) rounded down.at n=11A017919
- Powers of fourth root of 5 rounded down.at n=22A018057
- Ordered sequence of distinct terms of the form floor(x^i * floor(x^j)), i,j >= 0, where x = sqrt(5).at n=34A022770
- a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t(n)=2*n+1 (odd numbers).at n=33A023865
- a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n-k+1), where k = floor(n/2), s = natural numbers, t = odd natural numbers.at n=32A024862
- a(n) = (d(n)-r(n))/2, where d = A026063 and r is the periodic sequence with fundamental period (1,1,0,1).at n=33A026064
- Number of decimal digits in n-th Mersenne prime.at n=25A028335
- 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 83.at n=11A031581
- a(n) = floor(n^3 / Pi).at n=28A032633
- Cycle of 2 steps possible for 'concatenate a(n) and nextprime(a(n)) is a prime'.at n=42A034592
- Numerators of continued fraction convergents to sqrt(394).at n=8A041748
- Denominators of continued fraction convergents to sqrt(457).at n=10A041871
- a(n) = Sum_{k=1..floor((n+1)/2)} T(n,2k-1), array T as in A049777.at n=33A049778
- Smallest value of x such that M(x) = -n, where M(x) is Mertens's function A002321.at n=26A051401
- Inverse Mertens function: smallest k such that |M(k)| = n, where M(x) is Mertens's function A002321.at n=26A051402
- An inverse to Mertens's function: smallest k >= 2 such that Mertens's function |M(k)| (see A002321) is equal to n.at n=27A060434
- a(n) = floor(T(n+1)!*T(n-1)!/(T(n)!)^2), where T(n) = n(n+1)/2 = the n-th triangular number.at n=42A077539
- G.f.: ( x - 3*x^2 + 6*x^3 - 8*x^4 + 4*x^5 - x^7 ) / (1 - 4*x + 6*x^2 - 5*x^3 + 2*x^4 + x^5 - x^6 + x^7 ).at n=16A083839
- Divisors of 10^16 - 1.at n=32A111211
- Number of permutations of length n which avoid the patterns 2431, 3124, 3421.at n=8A116778