7712
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 17
- Digital Root
- 8
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 4
Divisibility
- Divisor Count
- 12
- Divisor Sum
- 15246
- Proper Divisor Sum (Aliquot Sum)
- 7534
- 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
- 3840
- Möbius Function
- 0
- Radical
- 482
- Omega Function (Ω)
- 6
- Little Omega Function (ω)
- 2
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
- 26
- Smith Number
- yes
- 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
- Number of n-bead necklaces with 2 colors when turning over is not allowed; also number of output sequences from a simple n-stage cycling shift register; also number of binary irreducible polynomials whose degree divides n.at n=17A000031
- Prefix (or Levenshtein) codes for natural numbers.at n=32A010097
- a(n) = floor( n*(n-1)*(n-2)/28 ).at n=61A011910
- 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 43.at n=26A031541
- Fibonacci iteration starting with (1, a(n)) leads to a "nine digits anagram".at n=13A034587
- Number of partitions of n with equal number of parts congruent to each of 1 and 2 (mod 4).at n=45A035543
- Number of partitions satisfying cn(1,5) + cn(4,5) <= cn(0,5) + cn(2,5) and cn(1,5) + cn(4,5) <= cn(0,5) + cn(3,5).at n=39A039864
- Triangle: Number of quasigroups of order n with k idempotents.at n=25A058175
- Triangle: Number of asymmetric quasigroups of order n with k idempotents.at n=25A058176
- Number of subsets of {1,2,...,n} which sum to 0 modulo n.at n=16A063776
- Number of subsets of {1,2,3,...,n} that sum to 0 mod 17.at n=17A068038
- a(1)=1, a(n) is the smallest integer > a(n-1) such that the largest element in the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals prime(n).at n=25A070901
- a(n) = (1/n) * Sum_{d divides n} (-1)^(n+d)*phi(n/d)*2^d.at n=16A074763
- Bisection of A000031.at n=8A100447
- Numbers n such that a(A109849(n)) = n.at n=46A109850
- Column 11 of table A105552.at n=15A110554
- Integers i such that 16*i XOR 17*i = 33*i.at n=38A115833
- a(n) = Sum_[k unrelated to n and k<n] a(k) = Sum_[k < n such that GCD(k,n) != 1 and k does not divide n ] a(k); a(1) = a(2) = a(3) = a(4) = 1.at n=31A118657
- Counts 2-wild partitions. In general p-wild partitions of n are defined so that they are in bijection with geometric equivalence classes of degree n algebra extensions of the p-adic field Q_p. Here two algebra extensions are equivalent if they become isomorphic after tensoring with the maximal unramified extension of Q_p.at n=11A131139
- a(n) = A159553(n)/n.at n=16A159554