13001
domain: N
Properties
Digital Properties
- Digit Count
- 5
- Digit Sum
- 5
- Digital Root
- 5
- Palindromic Number
- no
- Repdigit
- no
- Automorphic
- no
- Kaprekar Number
- no
- Multiplicative Persistence
- 1
Divisibility
- Divisor Count
- 2
- Divisor Sum
- 13002
- 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
- 13000
- Möbius Function
- -1
- Radical
- 13001
- 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
- 125
- 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
- yes
- Mersenne Prime
- no
- Sophie Germain Prime
- yes
- Safe Prime
- no
- Powerful Number
- no
- Achilles Number
- no
- Prime Index
- 1548
- Perfect Power
- no
- Smooth Number
- no
- Carmichael Number
- no
Classification
- Even
- no
- Odd
- yes
Appears in sequences
- Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime.at n=12A007530
- Initial terms of '4-block' primes as described in A032591.at n=18A032592
- Start of a string of exactly 2 consecutive (but disjoint) pairs of twin primes.at n=28A035790
- Primes at which the difference pattern X,2,4,2,Y (X and Y >= 6) occurs in A001223.at n=5A052165
- Primes associated with A052507.at n=36A052480
- Expansion of (1-x)*(1+x)/(1-2*x-x^2+x^3).at n=12A052534
- Primes p for which the period of reciprocal = (p-1)/8.at n=21A056213
- Primes of the form k^2 + 5.at n=8A056905
- Primes whose sum of digits is 5.at n=21A062341
- Primes of form 100*k + 1.at n=39A062800
- Let u be any string of n digits from {0,1}; let f(u) = number of distinct primes, not beginning with 0, formed by permuting the digits of u to a base-2 number; then a(n) = max_u f(u).at n=20A065843
- Lowest primes in twin packs.at n=35A069457
- Primes with arithmetic mean of digits = 1 (sum of digits = number of digits).at n=11A069710
- Totally balanced decimal numbers: if we assign the weight w(d) = d-1 to each digit d (i.e., w(0) = -1, w(1) = 0, ..., w(9) = 8) and then read the digits of the term from left to right, the partial sum of the weights is never negative and the total weighted sum is zero.at n=32A071154
- Łukasiewicz words that are also valid asynchronic siteswap juggling patterns.at n=25A071160
- Integers whose decimal expansion satisfies the condition that if we read each term from the left to right (the most significant to the least significant digit) then each nonzero digit gives a distance to the next nonzero digit to right (with a cyclic wrap-over from the least-significant to the most significant nonzero digit).at n=22A071161
- Duplicate of A069710.at n=11A073903
- Prime numbers such that first reversing digits and after squaring equals the result of first-squaring and after-reversing. Primes in A085305.at n=27A085306
- a(1) = 1, then the smallest prime divisor of A065447(n) not included earlier.at n=29A087552
- a(n) = if Floor[(2*Pi/E)*m^2] is prime then Floor[(2*Pi/E)*m^2].at n=7A090434