13513
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 13
- Digital Root
- 4
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 3
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 13514
- Proper Divisor Sum (Aliquot Sum)
- 1
- Abundant Number
- no
- Perfect Number
- no
- Deficient Number
- yes
- Weird Number
- no
- Untouchable Number
- no
- Primitive Abundant
- no
Derived Values
- Euler's Totient
- 13512
- Möbius Function
- -1
- Radical
- 13513
- Omega Function (Ω)
- 1
- Little Omega Function (ω)
- 1
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
- 37
- Smith Number
- no
- Vampire Number
- no
Primality
- Prime
- yes
- Composite Number
- no
- Semiprime
- no
- Squarefree Number
- yes
- Prime Power
- yes
- Prime Factorization
- no
- Twin Prime
- no
- Mersenne Prime
- no
- Sophie Germain Prime
- no
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1601
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Prime numbers p such that the number of partitions of p is also a prime.at n=11A038601
- Numerators of continued fraction convergents to sqrt(564).at n=6A042080
- a(n) = Sum_{k=0..n} Stirling2(n,k)^2.at n=6A047797
- Prime number spiral (clockwise, Southeast spoke).at n=20A054564
- Fifth term of weak prime quintets: p(m-3)-p(m-4) < p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1).at n=29A054827
- Sixth term of weak prime sextet: p(m-4)-p(m-5) < p(m-3)-p(m-4) < p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1).at n=1A054833
- Primes p = prime(k) such that prime(k) + prime(k+5) = prime(k+1) + prime(k+4) = prime(k+2) + prime(k+3).at n=36A064101
- Least number k such that k has n anti-divisors.at n=41A066464
- Primes such that the sum of the squares of its digits is equal to the product of its digits.at n=1A067779
- Smallest prime with concatenation of first n odd numbers as leading digits.at n=2A068837
- Number of anti-divisors of n (A066272) sets a record.at n=23A073638
- Group the natural numbers such that the n-th group contains n terms and the group sum is the smallest possible prime: (2), (1, 4), (3, 5, 9), (6, 7, 8, 10), (11, 12, 13, 14, 17), (15, 16, 18, 19, 20, 21), ... Sequence gives group sums.at n=29A075345
- Number of preferential arrangements of n labeled elements when at least k=3 elements per rank are required.at n=10A102233
- a(n) = 104*n + 9977.at n=34A126978
- Primes of the form 210k + 73.at n=32A140857
- Primes congruent to 8 mod 37.at n=40A142117
- Primes congruent to 24 mod 41.at n=38A142221
- Primes congruent to 11 mod 43.at n=40A142260
- Primes congruent to 24 mod 47.at n=35A142375
- Primes congruent to 38 mod 49.at n=35A142446