6513
domain: N
Properties
Digital Properties
- Digit Count
- 4
- Digit Sum
- 15
- Digital Root
- 6
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 2
Divisibility
- Divisor Count
- 8
- Divisor Sum
- 9408
- Proper Divisor Sum (Aliquot Sum)
- 2895
- 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
- 3984
- Möbius Function
- -1
- Radical
- 6513
- 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
- no
- Narcissistic Number
- no
- Collatz Steps
- 44
- 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
- arctanh(arcsin(tanh(x)))=x+1/3!*x^3+9/5!*x^5+169/7!*x^7+6513/9!*x^9...at n=4A012130
- 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 52.at n=37A031550
- a(n) = n * prime(n).at n=38A033286
- Numbers whose base-5 representation contains exactly two 0's and three 2's.at n=30A045183
- Triangle: self-converse semigroups of order n with k idempotents.at n=34A058118
- Numbers k such that prime(k+2)-(k+2)*tau(k+2) = prime(k-2)-(k-2)*tau(k-2) where tau(k) = A000005(k) is the number of divisors of k.at n=20A067354
- Convolution of L(n+1) := A000204(n+1) (Lucas), n>=0, with L(n+6), n>=0.at n=7A067984
- Least k such that there are no middle divisors of k (A071090) through k+n.at n=11A071563
- Coefficient of q^2 in nu(n), where nu(0) = 1, nu(1) = b and, for n >= 2, nu(n) = b*nu(n-1) + lambda*(1 + q + q^2 + ... + q^(n-2))*nu(n-2) with (b,lambda) = (3,1).at n=8A074362
- a(n) = 2^n + 7^n + 8^n.at n=4A074544
- a(n) = (a(n-1)+a(n-2))/7^k, where 7^k is the highest power of 7 dividing a(n-1)+a(n-2).at n=39A078414
- Leading diagonal of A083173.at n=38A083174
- Least positive multiples of index n that can result from the self-convolution of a monotonically increasing sequence (A087148).at n=45A087149
- a(n) = (n^3 - 7*n + 12)/6.at n=33A105163
- G.f. sum{k>=0, (x^2/(1-x)^3)^(2^k-1)}.at n=13A119971
- Multiples of 13 containing a 13 in their decimal representation.at n=19A121033
- a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3,4,5 and at least one of digits 6,7,8,9.at n=3A125947
- Numbers of the form m = p1 * p2 * p3 where for each d|m we have (d+m/d)/2 prime and p1 < p2 < p3 each prime.at n=32A128284
- Least number k such that k*p(n)*(k*p(n)+1)-1, k*p(n)*(k*p(n)+1)+1, k*p(n)*(k*p(n)+3)-1 and k*p(n)*(k*p(n)+3)+1 are all primes, two pairs of twin primes, with p(i) = i-th prime.at n=15A139638
- Number of n X n binary arrays symmetric under horizontal reflection with all ones connected only in a 110-111-100 pattern in any orientation.at n=9A146181